Practice topic-wise Solid Mechanics (XE-D) previous year questions for GATE XE (Engineering Sciences) with the official answer key. Step-by-step explanations are coming soon.
All GATE XE (Engineering Sciences) papers
292 questions. Answers are shown only where the official answer key is available.
Year: 2025 | Marks: 1
Consider a spring-mass system with mass m and spring stiffness k as shown in the illustration. At time t=0, the mass is displaced by P units and the velocity of the mass is zero. The displacement of the mass, x(t), is measured from the equilibrium position. Which one of the following functions represent x(t)?
Answer: D. 𝑃𝑐𝑜𝑠(√𝑘 𝑚𝑡)
Year: 2025 | Marks: 1
A ball of mass 5m approaches a stationary ball of mass m with a horizontal velocity of 2 m/s from left to right. After a perfectly elastic central collision, the horizontal velocity of the heavier ball is 1 m/s from left to right. Which one of the following statements, regarding the velocity (in m/s) of the lighter ball after impact, is TRUE?
Answer: B. Moves from left to right at 5 m/s
Year: 2025 | Marks: 1
The Mohr’s circle corresponding to an infinitesimal element is shown in the figure. The plane PQ in the infinitesimal element, at an angle of 𝜃 from the x-axis, is in a state of pure shear. Which one of the following values of 𝜃 (in degrees) is CORRECT?
Answer: C. 45
Year: 2025 | Marks: 1
The two-dimensional state of stress, in an infinitesimal element, is given by 𝜎𝑥𝑥= 800 MPa, 𝜎𝑥𝑦= 300 MPa and 𝜎𝑦𝑦= 0 MPa. Which one of the following options is the maximum shear stress (in MPa) in the element?
Answer: A. 500
Year: 2025 | Marks: 1
Two cars P and Q are travelling on a straight path and are 60 m apart as shown in the figure; Car P is moving with a constant velocity of 36 kmph, while car Q is moving at a constant velocity of 18 kmph. At this instant, the driver in car P applies the brake and collision occurs with car Q after 30 seconds. Assuming uniform deceleration due to braking, which one of the following is the CORRECT velocity (in m/s) of the car P just before the collision?
Answer: D. 4
Year: 2025 | Type: MSQ | Marks: 1
The natural frequency of a spring-mass system is 10 rad/s. Which of the following statements is/are CORRECT?
Answer: B. The mass is 1.25 kg and the stiffness is 125 N/m.; C. The stiffness is 620 N/m and the mass is 6.2 kg.
Year: 2025 | Type: NAT | Marks: 1
Consider a beam with a square box cross-section as shown in the figure. The outer square has a length of 10 mm. The thickness of the section is 1 mm. The area moment of inertia about the x-axis is _____ mm4 (in integer).
Answer: 490 to 494
Year: 2025 | Type: NAT | Marks: 1
For a certain linear elastic isotropic material, the Young’s modulus is 140 GPa and the shear modulus is 50 GPa. The Poisson’s ratio for the material is _____ (rounded off up to two decimal places).
Answer: 0.40
Year: 2025 | Type: NAT | Marks: 1
A force of P = 100 N is applied at the ends of the pliers as shown in the figure. Neglecting friction, the force exerted by the upper jaw on the workpiece is _____ N (in integer).
Answer: 400
Year: 2025 | Marks: 2
Consider two blocks, P of mass 100 kg and Q of mass 150 kg, resting as shown in the figure. The angle 𝜃= 30°. The coefficient of friction between the two blocks is 0.2. Assume no friction exists at all other interfaces. The minimum force required to move the block P upward is W. Which one of the following options is closest to the CORRECT magnitude of W (in N)?
Answer: A. 862.2
Year: 2025 | Marks: 2
Which one of the following vertical columns, of circular cross-section, sustains the highest load without buckling?
Answer: C. Cantilever column with a length L and cross-section diameter 2d
Year: 2025 | Marks: 2
The figure shows a rod PQ, hinged at P, rotating counter-clockwise with a uniform angular speed of 15 rad/s. A block R translates along a slot cut out in rod PQ. At the instant shown the distance PR = 0.5 m and θ = 60o. The relative velocity of R with respect to the rod PQ is 5 m/s at the instant shown. The relative acceleration of R with respect to the rod PQ is zero at the instant shown. Which one of the following is the CORRECT magnitude of the absolute acceleration (in m/s2) of block R?
Answer: B. 187.5
Year: 2025 | Marks: 2
The frame shown in the figure is loaded at S with a force of 2000 N. The reactions at T are denoted by Tx and Ty, while the reaction at W is Wy. Neglect the weight of the members. Which one of the following options for the magnitudes of the forces (in N), Tx, Ty and Wy, is CORRECT?
Answer: D. Tx = 0, Ty = 500 and Wy = 1500
Year: 2025 | Marks: 2
A closed thin cylindrical tank with a mean diameter d = 300 mm and thickness t = 2 mm, is subjected to a uniform internal gas pressure p. The allowable shear stress on the curved wall of the tank is 70 MPa. Based on the Tresca criteria, which one of the following options for the maximum safe value of p (in MPa) is CORRECT?
Answer: C. 1.87
Year: 2025 | Type: MSQ | Marks: 2
An infinitesimal square element PQRS is shown in the figure. The x and y axes are also marked in the figure. The strains on the element are given by 𝜀𝑥𝑥= 500 × 10−6, 𝜀𝑦𝑦= 100 × 10−6 and 𝜀𝑥𝑦= 0. Which of the following statements is/are CORRECT?
Answer: A. Percentage change in length of the diagonal PR is 0.03.; B. Change in angle between PR and QS is 4 × 10−4 rad.; D. Percentage change in length of the diagonal QS is 0.03.
Year: 2025 | Type: MSQ | Marks: 2
The figure shows the stress distribution across an internal surface of a rectangular beam of height 30 mm and depth 10 mm. The normal stress distribution is given by the expression 𝜎𝑥𝑥= 200𝑦+ 500 N/mm2; y is the distance in mm from the centroidal axis of the beam. Assume that there is no variation in the stress distribution along the z-direction. Which of the following statements is/are CORRECT?
Answer: A. The net force in the x direction is 150 kN.; C. The net moment about the z axis is 4500 Nm.
Year: 2025 | Type: NAT | Marks: 2
A vertical column fixed at one end is subjected to a compressive axial load at the free end. The column’s section modulus, EI, is 9.82 × 105 Nm2 and the cross-section area is 7.85 × 10−3 m2. The length of the column is 2 m. The yield stress of the material is 145 MPa. If the column can fail either in buckling or by Tresca’s criterion, the maximum load that the structure can safely sustain is _____ kN (rounded off to one decimal place).
Answer: 603.5 to 607.5
Year: 2025 | Type: NAT | Marks: 2
A simply-supported beam, with a point load P = 150 kN at a distance of L/3 from the left end, is shown in the figure. The elastic-strain energy (U) of the beam is given by the following expression: U = 2 243 P2L3 EI where the section modulus, EI, is 16.66 × 105 Nm2 and the length of the beam L is 1 m. The deflection at the loading point is ____ mm (rounded off to two decimal places).
Answer: 1.46 to 1.50
Year: 2025 | Type: NAT | Marks: 2
A simply-supported beam has a circular cross-section with a diameter of 20 mm, area of 314.2 mm2, area moment of inertia of 7854 mm4 and a length L of 4 m. A point load P =100 N acts at the center and an axial load Q = 20 kN acts through the centroidal axis as shown in the figure. The magnitude of the offset between the neutral axis and the centroidal axis, at L/2 from the left, is __________ mm (rounded off to one decimal place).
Answer: 4.9 to 5.1
Year: 2025 | Type: NAT | Marks: 2
A massless cantilever beam, with a tip mass m of 10 kg, is modeled as an equivalent spring-mass system as shown in the figure. The beam is of length L = 1 m, with a circular cross-section of diameter d = 20 mm. The Young’s modulus of the beam material is 200 GPa. The natural frequency of the spring-mass system is _____ Hz (rounded off to two decimal places).
Answer: 3.43 to 3.47
Year: 2025 | Type: NAT | Marks: 2
An electric motor’s rotor is spinning at 1500 rpm when its load and power are cut- off. The rotor which has a mass of 50 kg and a radius of gyration of 200 mm, then coasts down to rest. Due to kinetic friction, a constant torque of 10 Nm acts on the rotor as it coasts down. The number of revolutions executed by the rotor before it comes to rest is _____ (in integer).
Answer: 392 to 394
Year: 2025 | Type: NAT | Marks: 2
A bar of length L = 1 m is fixed at one end. Before heating its free end has a gap of δ = 0.1 mm from a rigid wall as shown in the figure. Now the bar is heated resulting in a uniform temperature rise of 10 ℃. The coefficient of linear thermal expansion of the material is 20 × 10−6/ ℃ and the Young’s modulus of elasticity is 100 GPa. Assume that the material properties do not change with temperature. The magnitude of the resulting axial stress on the bar is ______ MPa (in integer).
Answer: 10
Year: 2024 | Marks: 1
The engineering stress (𝜎) vs. engineering strain (𝜀) curve obtained by conducting uniaxial tension test on a steel specimen is shown in the figure (the sketched curve is not to the scale). The specimen exhibits cup-and-cone failure within its gage length. Which point on the curve corresponds to the beginning of necking in the test specimen?
Answer: D. S
Year: 2024 | Marks: 1
An L-shaped rigid member is fixed at the midpoint of a simply-supported beam, as shown in figure (i). The member is subjected to a vertically downward force P at its free end. In an equivalent system, the member along with the applied load is replaced with a force Q = P and a moment M (see figure (ii)). Which of the following statements is correct? (Neglect the mass of the beam and of the rigid member)
Answer: A. M = P a
Year: 2024 | Marks: 1
A block of weight W, placed on a surface, is subjected to a horizontal force P as shown in the figure. The line of action of force P passes through the center-of- gravity of the block. The magnitude of P is such that the block remains at rest. If N is the resultant normal reaction exerted by the surface, and F is the frictional force acting on the bottom surface of the block, then which of the following represents the correct free body diagram of the block?
Answer: B.
Year: 2024 | Marks: 1
A mass M is hung from a frictionless, massless pulley. The pulley is suspended by using an inextensible, massless rope of which one end is directly fixed to a support, and the other end is connected to the support through a linear spring of stiffness constant k (see figure). The natural frequency of this system is
Answer: A. √4𝑘 𝑀
Year: 2024 | Marks: 1
A simply-supported beam of rectangular cross-section (width w and height h) is subjected to the loads as shown in the figure (i). The enlarged view of the beam cross-section is shown in figure (ii). The coordinate system is indicated in the figures. Assuming Euler-Bernoulli beam approximation, the shear stress 𝜏𝑥𝑧 and normal stress 𝜎𝑥𝑥 at the origin, O are respectively given by
Answer: D. 0 , 0
Year: 2024 | Marks: 1
An ice-skater starts spinning during her performance. As she retracts her arms and legs closer to her body, her angular velocity _________________.
Answer: A. increases
Year: 2024 | Type: MSQ | Marks: 1
A solid circular shaft of diameter 100 mm is subjected to a torque 3𝜋 kNm. Which of the following statements about the state of stress in the shaft is/are correct?
Answer: A. The maximum shear stress is 48 MPa; B. The maximum tensile stress is 48 MPa; C. The magnitude of maximum compressive stress is 48 MPa
Year: 2024 | Type: NAT | Marks: 1
A spring is connected to an elastic bar as shown in the figure. The spring has a stiffness constant of 107 N/m. The bar is 70 mm long, and has an area of cross- section 10 mm2. The Young’s modulus of the bar material is 70,000 MPa. A force F = 5000 N is applied at point O along the axis of the bar and the spring. The resulting deflection of Point O in mm (rounded to one decimal place) is ______
Answer: 0.9 to 1.1
Year: 2024 | Type: NAT | Marks: 1
A particle of mass 1 kg is attached to one end of a spring having stiffness of 125 N/m. The free length of the spring is 100 mm. The system is rotated about the other end of the spring at a uniform angular velocity of 5 rad/s. Ignore gravity and consider that the elongation of the spring may be comparable to the free length of the spring. The elongation of the spring (in mm, rounded off to the nearest integer) is ______ .
Answer: 24 to 26
Year: 2024 | Marks: 2
A 0-45-90 strain gauge rosette is mounted on an aircraft wing. The co-ordinate system is placed such that the strain gauges p, q and r are oriented at angles 0o, 45o and 90o, respectively, from the x axis (see figure). The strain readings associated to p, q and r are denoted by 𝜀𝑝, 𝜀𝑞, and 𝜀𝑟 , respectively. While conducting a test the strain gauges show the following readings. 𝜀𝑝= 150 × 10−6, 𝜀𝑞= 180 × 10−6, 𝜀𝑟= −90 × 10−6 The developed engineering shear strain 𝛾𝑥𝑦 associated to the strain gauge data is
Answer: C. 300 × 10−6
Year: 2024 | Marks: 2
A rigid bar PQR is hinged at its end P. As shown in the figure, the bar is pin- connected through two identical links QS and RT at points Q and R, respectively. The other ends of the links, S and T, are fixed. Both links are made of the same material. If the temperature of the links is uniformly increased by ΔT, then which one of the following statements is correct? (Neglect the weight of the rigid bar)
Answer: D. QS will be under compression and RT will be under tension.
Year: 2024 | Marks: 2
A pin-jointed truss has a pin support at the point E and a roller support at the point F. A horizontal force P is applied at pin H as shown in the figure. Which one of the members is in compression ?
Answer: C. EG
Year: 2024 | Marks: 2
Two identical rigid slender bars of length 2L and mass 𝑚 are acted upon by a transverse force F at one of the ends as shown in the figure. In the first case, the bar is pinned at the other end. In the second case, the bar is pinned at its mid-point. What should be the magnitude of the force F such that the resulting angular accelerations of the two bars are equal?
Answer: B. 𝑚𝑔 2
Year: 2024 | Type: MSQ | Marks: 2
A critical point on a component is subjected to the state of stress [𝜎] as given in the following. The yield strength of the material is 400 MPa. By considering maximum shear stress (Tresca) theory, the possible value(s) of 𝜎0 at the onset of yielding is/are, [𝜎] =[ 280 0 0 0 𝜎𝑜 0 0 0 −60 ] MPa
Answer: A. 340; C. ̶ 120
Year: 2024 | Type: NAT | Marks: 2
A plane passing through a point Q inside a body is shown. The unit normal of the plane is 𝑛̂ = 0.6𝑖̂ + 0.8𝑗̂ , as shown in the figure. The traction (stress) vector on the plane at point Q is given by 𝑡 = (50𝑖̂ + 20𝑗̂) MPa. Given that at point Q, 𝜎𝑥𝑥= 𝜎𝑦𝑦 , the shear stress component 𝜏𝑥𝑦 (in MPa, rounded off to two decimal places) is ___________ .
Answer: 99.00 to 101.00
Year: 2024 | Type: NAT | Marks: 2
A rigid massless bar PQR is hinged at its end P and supported through a spring of stiffness k at point Q. A vertically downward force W = 560 N is applied at the free end R of the bar. If the vertical component of the displacement at R is 30 mm, then the stiffness of the spring (in kN/m, rounded off to one decimal place) is ___.
Answer: 41.0 to 43.0
Year: 2024 | Type: NAT | Marks: 2
A beam of rectangular cross-section, as shown in the figure, is made of two perfectly bonded layers of different materials and equal thickness. The Young’s moduli of the two materials are 𝐸1 and 𝐸2, where 𝐸1 = 2𝐸2. The beam is subjected to pure bending. If t = 1 mm, the distance of the neutral plane from the top surface of the beam is ______ (in mm, rounded off to two decimal places).
Answer: 0.80 to 0.85
Year: 2024 | Type: NAT | Marks: 2
A stepped beam is made of a material whose Young’s modulus is E. The dimensions of the two stepped sections are such that the sectional moments of inertia, 𝐼1and 𝐼2, are related as 𝐼1 = 8𝐼2. The beam is fixed at one end and a load of F is applied at the free end as shown in the figure. Under this loading condition, if the strain energy of the stepped beam is written as 𝑈= 𝛽 𝐹2𝐿3 𝐸𝐼1 , then the value of 𝛽 is ________ (rounded off to two decimal places).
Answer: 0.29 to 0.33
Year: 2024 | Type: NAT | Marks: 2
A cylindrical pressure vessel is constructed by bolting two symmetric halves of flanged semi-cylindrical shells. A cross-sectional view of the vessel is shown in the figure. The inner diameter of the vessel is 2 m and the length is 10 m. Each row comprises 100 bolts along the length of the vessel. If the vessel is pressurized to a net pressure of 6 x 105 N/m2, and assuming the end caps of the vessel do not take any load in the radial direction, then the load borne by each bolt is __________ (in kN, rounded off to one decimal place)
Answer: 59.5 to 60.5
Year: 2024 | Type: NAT | Marks: 2
A turn-table is rotating about its center with an angular velocity of 2 rad/s in the counter-clockwise direction. There is a groove in the turn-table within which a marble moves with a constant speed v m/s relative to the turn-table. At a given instant, the marble is at a radial distance of 1 m from the center and the line joining the center of the turn-table with the marble makes an angle of 30° with the groove. The value of v (in m/s, rounded off to one decimal place) for which there is no radial acceleration for the marble at this instant is _____.
Answer: 1.9 to 2.1
Year: 2024 | Type: NAT | Marks: 2
The system shown in the figure is in static equilibrium. The spring is massless and has a spring constant of K=1 kN/m. The free length of the spring is 1 m. All bodies in the system except the spring are rigid and have mass of M=1 kg. All surfaces are frictionless and pin joints are ideal. The elongation of the spring (in mm, rounded off to the nearest integer) in this configuration is ______. Take the acceleration due to gravity 𝑔= 10 m/s2.
Answer: 14 to 16
Year: 2024 | Type: NAT | Marks: 2
A square block of side 1 m and mass 10 kg is resting on a horizontal surface. The coefficient of static friction between the block and the surface is 0.75. A horizontal force P acts on the block as shown in the figure. The force P is gradually increased from zero until the block either slides or topples. The maximum value of ℎ (in m, rounded off to two decimal places) for which the block slides without toppling is _____. Take the acceleration due to gravity 𝑔= 10 m/s2.
Answer: 0.66 to 0.68
Year: 2023 | Marks: 1
A plane truss is simply supported at P and R as shown. A downward force F is applied at hinge Q. The axial force developed in member PS is
Answer: B. √5 2 𝐹 Compressive
Year: 2023 | Marks: 1
A massless rigid rod OP of length L is hinged frictionlessly at O. A concentrated mass m is attached to end P of the rod. Initially, the rod OP is horizontal. Then, it is released from rest. There is gravity as shown. The rod acquires an angular velocity as it swings. The clockwise angular velocity of the rod, when it first reaches the vertical position as shown, is
Answer: B. √ 2 𝑔 𝐿
Year: 2023 | Marks: 1
Two equivalent descriptions of the state of stress at a point are shown in the figure. The normal stresses 𝜎1 and 𝜎2 as shown on the right must be, respectively,
Answer: A. 𝜏o and −𝜏o
Year: 2023 | Marks: 1
The state of strain at a point in a machine component is given as 𝜀𝑥𝑥= 2.5 × 10−4, 𝜀𝑦𝑦= 2.0 × 10−4, 𝜀𝑧𝑧= −1.5 × 10−4, 𝜀𝑥𝑦= 2.5 × 10−4, 𝜀𝑦𝑧= −0.5 × 10−4, 𝜀𝑧𝑥= −1.0 × 10−4. The volumetric strain at this point is
Answer: B. 3 × 10−4
Year: 2023 | Marks: 1
A thin walled, closed cylindrical vessel of inside diameter 𝑑 and wall thickness 𝑡 contains a fluid under pressure 𝑝. The figure below shows a part of the cylindrical vessel; end caps are not shown. Consider the small element shown with sides parallel and perpendicular to the axis of the cylinder. The stresses 𝜎1 and 𝜎2 are
Answer: A. 𝜎1 = 𝑝𝑑 2𝑡; 𝜎2 = 𝑝𝑑 4𝑡
Year: 2023 | Type: MSQ | Marks: 1
A spring mass system is shown in the figure below. Take the acceleration due to gravity as 𝑔 = 9.81 m/s2. The static deflection due to weight and the time period of oscillations, respectively, are
Answer: A. 0.392 m and 1.26 s
Year: 2023 | Type: NAT | Marks: 1
A rod is subjected to three forces as shown in the figure on the left. An equivalent force system with forces F1, F2 and moment M is shown in the figure on the right. The value of M (in N-m) is______(rounded off to one decimal place).
Answer: 117.0 to 118.0
Year: 2023 | Type: NAT | Marks: 1
A simply supported beam of length 3 m is loaded as shown in the figure. The magnitude of the shear force (in kN) at the mid-point of the beam is______(rounded off to one decimal place).
Answer: 4.9 to 5.1
Year: 2023 | Type: NAT | Marks: 1
For a plane stress problem, the principal stresses are 100 MPa and 50 MPa. The magnitude of maximum shear stress (in MPa) in the material is______(rounded off to one decimal place).
Answer: 49.5 to 50.5
Year: 2023 | Marks: 2
A solid uniform rigid disk of mass 𝑚 and radius 𝑅 rolls without slipping along a horizontal surface PQ. The speed of the center of the disk is 𝑣. The disk then strikes a hurdle of height 3𝑅 20 at point S. During the impact, there is no rebound or slip at S and no impulse from the surface PQ. The magnitude of the velocity of the center of the disk immediately after the impact is
Answer: D. 0.9𝑣
Year: 2023 | Marks: 2
A cylinder made of rubber (length = L and diameter = d) is inserted in a rigid container as shown in the figure. The rubber cylinder fits snugly in the rigid container. There is no wall friction. The modulus of elasticity of the rubber is E and its Poisson’s ratio is ν. The cylinder is subjected to a small uniform pressure 𝑝 as shown in the figure. The resulting axial strain (𝜀𝑧𝑧) is
Answer: C. − 𝑝 𝐸[(1 + ν)(1 −2ν) (1 −ν) ]
Year: 2023 | Marks: 2
The state of stress at the critical location in a structure is 𝜎𝑥𝑥 = 420 MPa, 𝜎𝑦𝑦 = 100 MPa, 𝜎𝑧𝑧= 𝜎𝑥𝑦 = 𝜎𝑦𝑧= 𝜎𝑧𝑥= 0. The yield stress of the material in uniaxial tension is 400 MPa. Select the correct statement among the following.
Answer: C. The structure is unsafe by Tresca (maximum shear stress) theory and safe by von-Mises (distortion energy) theory.
Year: 2023 | Marks: 2
The figure shows a column of rectangular cross section 100 mm × 80 mm. It carries a load of 60 kN at a point 30 mm from the edge 𝑃𝑄. The values of stress component 𝜎𝑧𝑧 on surfaces 𝑃𝑄𝑄′𝑃′ and 𝑆𝑅𝑅′𝑆′, at points far away from both ends of the column, are respectively
Answer: D. 13.13 N/mm2 (Compressive) and 1.88 N/mm2 (Compressive)
Year: 2023 | Marks: 2
Consider an electric pole with dimensions as shown in the figure. Let the end R be subjected to a vertical force F. The flexural rigidity of both vertical and horizontal bars is EI. Neglect the axial deflection of the vertical bar, and all effects of self-weight. The vertical deflection at end R is
Answer: A. 7𝐹𝐿3 3𝐸𝐼
Year: 2023 | Type: MSQ | Marks: 2
A uniform cantilever beam has flexural rigidity 𝐸𝐼 and length 𝐿. It is subjected to a concentrated force 𝐹 and moment 𝑀= 2𝐹𝐿 at the free end as shown. The deflection (𝛿) at the free end is
Answer: C. 4𝐹𝐿3 3𝐸𝐼
Year: 2023 | Type: NAT | Marks: 2
A steel ball of mass 𝑚 = 10 kg is suspended from the ceiling of a moving carriage by two inextensible strings making 60° with the horizontal as shown. The carriage has an acceleration 𝑎 such that the tension in the string on the right is double the tension in the string on the left. Take the acceleration due to gravity (g) as 10 m/s2. The acceleration 𝑎 (in m/s2) is______(rounded off to one decimal place).
Answer: 1.8 to 2.0
Year: 2023 | Type: NAT | Marks: 2
A block of mass 𝑚= 10 kg is lying on an inclined plane PQ. The mass is restrained from sliding down the inclined plane by a force 𝐹. The coefficient of friction between the block and the inclined plane is 0.3. Take the acceleration due to gravity as 10 m/s2. The smallest force 𝐹 (in N) required to prevent the block from sliding down is______(rounded off to one decimal place).
Answer: 23.0 to 25.0
Year: 2023 | Type: NAT | Marks: 2
A spherical rigid ball of mass 10 kg is moving with a speed of 2 m/s in the direction shown. The ball collides with a rigid frictionless wall and rebounds at an angle 𝛼 with a speed of 𝑣, as shown. The coefficient of restitution is 0.9. The angle 𝛼 (in degrees) is______(rounded off to one decimal place).
Answer: 57.0 to 58.0
Year: 2023 | Type: NAT | Marks: 2
A thin steel plate is loaded in the x-y plane as shown in the figure. Take the Poisson’s ratio of steel to be 0.3 and the modulus of elasticity of steel to be 200 GPa. The strain along the 𝑧-direction is 𝜀𝑧𝑧= −3 × 10−4. The value of 𝜎𝑦𝑦 (in MPa) is______(rounded off to one decimal place).
Answer: 79.5 to 80.5
Year: 2023 | Type: NAT | Marks: 2
A composite rod made of steel and copper is fixed immovably at its ends as shown in the figure. The length of each portion of the rod is 1 m as shown. The cross-sections of both portions are the same. The moduli of elasticity of steel and copper are 200 GPa and 100 GPa, respectively. The coefficients of thermal expansion of steel and copper are 12 × 10−6 /℃ and 18 × 10−6 /℃, respectively. The composite rod is initially stress free. Then, the temperature of the composite rod is increased by 100 ℃. The magnitude of axial stress (in MPa) developed in the steel rod is______(rounded off to one decimal place).
Answer: 199.0 to 201.0
Year: 2023 | Type: NAT | Marks: 2
A slender uniform elastic rod of length 1 m and of solid circular cross-section of diameter 50 mm is originally straight. It is then loaded by equal and opposite end moments as indicated in the figure. The resulting lateral displacement of the mid-point of the rod is 10 mm (displacements are exaggerated in the figure). The maximum longitudinal strain in the rod is 𝑝 × 10−3, where 𝑝 is______(rounded off to one decimal place).
Answer: 1.9 to 2.1
Year: 2023 | Type: NAT | Marks: 2
Consider a solid cylindrical shaft and a hollow cylindrical shaft. Both shafts are axisymmetric and elastic, and have the same cross-sectional area. The hollow shaft has an outside diameter of 150 mm and an inside diameter of 120 mm. When both the shafts are twisted by the same twisting moment, the ratio of maximum shear stress developed in the hollow shaft (𝜏ℎ) to maximum shear stress developed in the solid shaft (𝜏𝑠) will be______(rounded off to three decimal places).
Answer: 0.350 to 0.380
Year: 2022 | Marks: 1
A force 𝐹 is applied at an angle 𝜃ൌ30 on an elastic column as shown in the figure. 𝐸 and 𝐼 are respectively the Young’s modulus and area moment of inertia. The smallest magnitude of 𝐹 needed to cause buckling is
Answer: A. ଶ √ଷ గమாூ మ
Year: 2022 | Marks: 1
The shear stress due to a transverse shear force in a linear elastic isotropic beam of rectangular cross-section
Answer: C. is maximum at the neutral axis
Year: 2022 | Marks: 1
A massless semicircular rod held fixed at end A is in the xy-plane, as shown in the figure. A force P along the negative z direction is acting at point B on the rod. The unit vectors along x, y and z directions are denoted respectively as i, j and k. Due to the applied force P, the cross-section of the rod at point D will be subjected to
Answer: A. a twisting moment 𝑃𝑅ሺ1 െcos 𝜃ሻ𝐢, a bending moment 𝑃𝑅sin 𝜃 𝐣, and a shear force െ𝑃 𝐤
Year: 2022 | Marks: 1
In the truss shown in the figure, all the members are pin jointed to each other. The members AB, BD, DE and DC have the same length. For the given loading, which of the following is the correct statement?
Answer: B. AB is in tension, ED is in compression, and BD is a zero-force member
Year: 2022 | Marks: 1
End B of the 2 m long rigid rod AB is constrained to move horizontally in the slot as shown in the figure and has a velocity of 1.0 i m/s. The angular velocity of the rod at the instant shown is 2 rad/s. The unit vectors along x and y directions are denoted respectively as i and j. The velocity of point A in m/s is then given by
Answer: A. ൫1 െ2√3൯𝐢2𝐣
Year: 2022 | Marks: 1
The assembly of four masses connected by rigid mass-less rods is kept on a smooth horizontal floor as shown in the figure. Under the applied force 2F, the magnitude of angular acceleration of the assembly at the instant shown is
Answer: B. 𝐹 2𝑚𝑐
Year: 2022 | Marks: 1
A particle is constrained to move at a constant speed on an inclined plane (ABCD) along the curved path shown in the figure. Edges AD and BC are parallel to the y axis. The inclined plane makes an angle 𝜃 with the 𝑥𝑦-plane. The velocity vector of the particle makes an angle 𝜙 with the dotted line which is parallel to edge AB. If the speed of the particle is 2 m/s, 𝜙ൌ30°, and 𝜃ൌ40°, then the 𝑧-component of the velocity of the particle in m/s is __________
Answer: C. െ1.11
Year: 2022 | Type: NAT | Marks: 1
A uniform elastic rod of constant cross-section is fixed at its left end as shown in the figure. An axial force 𝑃 is acting as shown. Assume that plane sections remain plane during deformation. The ratio of axial displacements at point A ሺ𝑥ൌ4𝐿ሻ to that at point B ሺ𝑥ൌ𝐿ሻ is ______ (rounded off to one decimal place)
Answer: 1.9 to 2.1
Year: 2022 | Type: NAT | Marks: 1
A thin-walled spherical pressure vessel has a mean radius of 500 mm and wall thickness of 10 mm. The yield strength of the material is 500 MPa. The internal pressure in MPa at which the spherical pressure vessel will yield according to the Tresca criterion is ____________ (rounded off to one decimal place)
Answer: 19 to 21
Year: 2022 | Marks: 2
The beam in the figure is subjected to a moment M0 at mid span as shown. Which of the following is the vertical reaction at B?
Answer: A. 0 9 8 M L
Year: 2022 | Marks: 2
A spring-mass system having a mass m and spring constant k, placed horizontally on a foundation, is connected to a vertically hanging mass m with the help of an inextensible string. Ignore the friction in the pulleys and also the inertia of pulleys, string and spring. Gravity is acting vertically downward as shown. The natural frequency of the system in rad/s is
Answer: D. ඨ4𝑘 5𝑚
Year: 2022 | Marks: 2
One end of a uniform rigid rod OA of length L and mass m is attached to a frictionless hinge at O. The other end of the rod is connected to the roof at B with a mass-less inextensible thread AB. Initially the rod is horizontal and at rest. The gravity is acting vertically downward as shown. Immediately after the thread AB is cut, the reaction on the rod at O is
Answer: A. ସ in the positive y-direction
Year: 2022 | Marks: 2
A circular shaft is rigidly connected to a wall at one end. The shaft has a solid portion and a hollow portion as shown in the figure. The length of each portion is 𝐿 and the shear modulus of the material is 𝐺. The polar moment of inertia of the hollow portion is 𝐽 and that of the solid portion is 50𝐽. A torque 𝑇 is applied at the right most end as shown. The rotation of the section PQ is
Answer: A. ଶ் ଵீ
Year: 2022 | Marks: 2
A rectangular plate of uniform thickness having initial length a and width b is placed between two rigid immovable walls. The temperature of the plate is increased by ΔT. The plate is free to expand along the y and z directions. The mid-surface of the plate remains in the xy-plane. The Poisson’s ratio is ν and the coefficient of thermal expansion is α. Assuming that the plate is initially free of stresses, the change in length of the plate after the increase in temperature is given by
Answer: B. (1 ) a T να + Δ
Year: 2022 | Marks: 2
A mass m = 10 kg is attached to a spring as shown in the figure. The coefficient of friction between the mass and the inclined plane is 0.25. Assume that the acceleration due to gravity is 10 m/s2 and that static and kinematic friction coefficients are the same. Equilibrium of the mass is impossible if the spring force is
Answer: A. 30 N
Year: 2022 | Type: NAT | Marks: 2
The frame shown in the figure is subjected to a uniformly distributed load of 1000 N/m over a distance of 0.6 m. Neglecting the weight of the frame, the maximum shear force (in N) in the region between the supports A and B of the frame is ________.
Answer: 295 to 305
Year: 2022 | Type: NAT | Marks: 2
A slider moving in a frictionless slot is connected with a linear spring OA as shown in the figure. The following is known: stiffness of the spring = 2 kN/m, mass of the slider = 10 kg, and the unstretched length of the spring = 1 m. If the slider is released from rest at A the magnitude of its velocity (in m/s) when it passes through point B is ____________(rounded off to the nearest integer)
Answer: 39 to 41
Year: 2022 | Type: NAT | Marks: 2
A sphere A of mass 𝑚 is thrown into the air at 50 m/s along a direction tanିଵሺ3/4ሻ up from the horizontal. At the topmost point of its trajectory, it has a central (non- oblique) collision with another sphere B which is at rest on top of a vertical pole. Sphere B has a mass of 3𝑚. Acceleration due to gravity is 10 m/s2. Neglect contact friction and air-resistance. If the coefficient of restitution is 0.3, then the speed (in m/s) of sphere A immediately after the collision is_________ (rounded off to one decimal place)
Answer: 0.9 to 1.1
Year: 2022 | Type: NAT | Marks: 2
The truck shown in the figure is moving on a horizontal road at a speed of 20 m/s. It is carrying a box of mass 1000 kg, which is simply placed on the truck platform. The coefficient of friction between the truck platform and the box is 0.25. Take acceleration due to gravity as 10 m/s2. Assume uniform deceleration during braking, and the coefficients of static and kinetic friction to be the same. The shortest distance in meters in which the truck can be brought to rest without the box slipping is _______(round off to the nearest integer)
Answer: 79 to 81
Year: 2022 | Type: NAT | Marks: 2
The stepped rod of length 2 m, shown in the figure, is fixed at both ends (A and C). The area of cross-section of portion AB is 200 mm2 and that of portion BC is 100 mm2. Force F is applied at section B such that the section is displaced by 0.1 mm in the direction of the force. Young’s modulus of the rod is 200 GPa. The applied force F in N is _______ (round off to the nearest integer)
Answer: 5990 to 6010
Year: 2022 | Type: NAT | Marks: 2
A cantilever beam has a span of 1 m and carries a uniformly distributed load of q = 1250 N/m over a portion as shown. A force F =1000 N acts at a distance L from the fixed end. The distance L is such that the bending moment at the fixed end is zero. The beam has a rectangular cross-section of depth 20 mm and width 24 mm. For this loading, the magnitude of the maximum bending stress in the beam in MPa is________________(round off to the nearest integer)
Answer: 123 to 127
Year: 2022 | Type: NAT | Marks: 2
The figure shows two identical mass-less beams AB and CD, each clamped at one of their ends. The left end of beam CD rests on the right end of beam AB such that the ends of the beams are just in contact. The beams are unstressed before the application of load. Assume no friction at the contact. Now, if a uniformly distributed load of 800 N/m is applied on beam CD, the bending moment at the end B of beam AB in N.m is ___________ (rounded off to the nearest integer)
Answer: 148 to 152
Year: 2020 | Marks: 1
GATE XE 2020, Solid Mechanics, Q.1: see the question image.
Answer: D.
Year: 2020 | Marks: 1
GATE XE 2020, Solid Mechanics, Q.2: see the question image.
Answer: C.
Year: 2020 | Marks: 1
GATE XE 2020, Solid Mechanics, Q.3: see the question image.
Answer: B.
Year: 2020 | Marks: 1
GATE XE 2020, Solid Mechanics, Q.4: see the question image.
Answer: B.
Year: 2020 | Marks: 1
GATE XE 2020, Solid Mechanics, Q.5: see the question image.
Answer: A.
Year: 2020 | Marks: 1
GATE XE 2020, Solid Mechanics, Q.6: see the question image.
Answer: B.
Year: 2020 | Type: NAT | Marks: 1
GATE XE 2020, Solid Mechanics, Q.7: see the question image.
Answer: 6.25 to 6.40
Year: 2020 | Type: NAT | Marks: 1
GATE XE 2020, Solid Mechanics, Q.8: see the question image.
Answer: 90
Year: 2020 | Type: NAT | Marks: 1
GATE XE 2020, Solid Mechanics, Q.9: see the question image.
Answer: 150
Year: 2020 | Marks: 2
GATE XE 2020, Solid Mechanics, Q.10: see the question image.
Answer: D.
Year: 2020 | Marks: 2
GATE XE 2020, Solid Mechanics, Q.11: see the question image.
Answer: A.
Year: 2020 | Marks: 2
GATE XE 2020, Solid Mechanics, Q.12: see the question image.
Answer: B.
Year: 2020 | Marks: 2
GATE XE 2020, Solid Mechanics, Q.13: see the question image.
Answer: D.
Year: 2020 | Marks: 2
GATE XE 2020, Solid Mechanics, Q.14: see the question image.
Answer: A.
Year: 2020 | Type: NAT | Marks: 2
GATE XE 2020, Solid Mechanics, Q.15: see the question image.
Answer: 9.99 to 10.00
Year: 2020 | Type: NAT | Marks: 2
GATE XE 2020, Solid Mechanics, Q.16: see the question image.
Answer: 18.60 to 18.90
Year: 2020 | Type: NAT | Marks: 2
GATE XE 2020, Solid Mechanics, Q.17: see the question image.
Answer: 4.477 to 4.487
Year: 2020 | Type: NAT | Marks: 2
GATE XE 2020, Solid Mechanics, Q.18: see the question image.
Answer: 7
Year: 2020 | Type: NAT | Marks: 2
GATE XE 2020, Solid Mechanics, Q.19: see the question image.
Answer: 10.160 to 10.340
Year: 2020 | Type: NAT | Marks: 2
GATE XE 2020, Solid Mechanics, Q.20: see the question image.
Answer: 5.600 to 5.650
Year: 2020 | Type: NAT | Marks: 2
GATE XE 2020, Solid Mechanics, Q.21: see the question image.
Answer: 0.175 to 0.190
Year: 2020 | Type: NAT | Marks: 2
GATE XE 2020, Solid Mechanics, Q.22: see the question image.
Answer: 1.90 to 2.05
Year: 2018 | Marks: 1
A thin cylinder (thickness, ݐ and diameter, ) with closed ends is subjected to an internal pressure, . The ratio of hoop stress to longitudinal stress developed in the wall of the cylinder is
Answer: D. 2:1
Year: 2018 | Marks: 1
A steel rod is fixed at one end and free at the other end. The coefficient of thermal expansion of the steel is α, and modulus of elasticity is E. If the temperature of the rod is increased by ∆ܶ then the stress and strain developed in the rod are respectively
Answer: A. zero, α∆ܶ
Year: 2018 | Marks: 1
The effective lengths of the columns with ideal boundary conditions shown in Case-I, Case-II, and Case-III are respectively
Answer: D. ܮ, 2ܮ, ܮ/2
Year: 2018 | Marks: 1
At a point in a stressed body, sum of the normal stresses acting on perpendicular faces of an arbitrarily oriented plane stress element is always
Answer: B. constant and independent of angle of orientation of the element
Year: 2018 | Marks: 1
The principal stresses on a plane stress element are shown in the figure. The maximum shear stress (in MPa) is
Answer: B. 100
Year: 2018 | Type: NAT | Marks: 1
A rigid and thin L-shaped bracket is fixed to the wall at point B, and a force F is applied at point A as shown. For a given force F, the point B experiences the maximum clockwise moment when the inclination θ (in degrees) with the x-axis is……….[up to two decimal places].
Answer: 52.50 to 53.50
Year: 2018 | Type: NAT | Marks: 1
A cantilever beam with length, L = 1 m, modulus of elasticity, E = 210 GPa, and area moment of inertia, I = 1.2 ൈ10ିm4 carries a concentrated mass m = 100 kg at its free- end. By idealizing it as a single degree-of-freedom system and neglecting the mass of the cantilever beam, the natural frequency (in rad/s) of small transverse oscillations of the mass m is …….. [up to two decimal places]
Answer: 27.00 to 28.00
Year: 2018 | Type: NAT | Marks: 1
For a typical grade of steel, the value of modulus of elasticity (E) and Poisson’s ratio (ν) are 208 GPa and 0.3 respectively. The value of shear modulus (G) of the steel (in GPa) is …….. 8 mm P = 20 kN P = 20 kN 50 mm
Answer: 80
Year: 2018 | Type: NAT | Marks: 1
A tensile test is performed on a metallic specimen of diameter 8 mm and gauge length 50 mm. When the tensile load P reaches a value of 20 kN, the distance between the gauge marks increases by 0.09 mm. If the sample remains within the elastic limit, the modulus of elasticity (in GPa) of the test metal is………..[up to two decimal places]
Answer: 220.00 to 222.00
Year: 2018 | Marks: 2
A beam ABC is subjected to load P at its free end C as shown in the figure. The flexural rigidity of the beam is ܧܫ. The vertical support reaction at point B is
Answer: B. ହ ଶ
Year: 2018 | Marks: 2
A horizontal effort P is applied to raise a block of weight W on a rough surface inclined at an angle θ with the horizontal. If ߤ௦ is the coefficient of static friction between the block and the surface, the minimum effort P required to impend the upward motion of the block along the surface is
Answer: B. ቀ ఓೞା௧ఏ ଵିఓೞ௧ఏቁ
Year: 2018 | Marks: 2
Three round bars of same material, equal lengths, and different cross-sectional dimensions are shown in the figures as Case-I, Case-II and Case-III. All the bars are clamped at the upper end, and a concentrated load P is applied at the lower end of each bar. If the elastic strain energy stored in the bar shown in Case-I is ଵ then the elastic strain energy stored in Case-II and Case-III respectively is
Answer: D. ቀ5 8 ൗቁܷ ଵ, ቀ5 8 ൗቁܷ ଵ Case-I Case-II Case-III 2d L d P 2d d L/4 L/2 L/4 d 2d d P P L/4 L/2 L/4
Year: 2018 | Marks: 2
A rigid uniform rod with mass m, length L and center of gravity G is freely suspended from a hinge as shown in the figure. The rod is given a small angular displacement θ in the counter-clockwise direction from the position in which it hangs vertically (θ = 0). If ݃ is the acceleration due to gravity, the natural frequency of oscillations (in rad/s) is
Answer: C. ට ଷ ଶ
Year: 2018 | Marks: 2
A cylindrical member, made up of ductile material, is subjected to pure torsion as shown in the figure. The failure plane (from Option-I to Option-IV) for ductile material as per maximum shear stress theory is represented by
Answer: C. Option III
Year: 2018 | Marks: 2
A simply supported beam of span L is subjected to a couple Mo at a distance a from support A. Among the four options (Option-I to Option-IV) shown, the correct shear force diagram of the beam is
Answer: A. Option-I
Year: 2018 | Marks: 2
A circular shaft ABC of diameter, ݀ and length, ܮ is fixed at end A. It is subjected to the torsional moments at point B and point C as shown in the figure. The ratio of angle of twists at point B to point C is
Answer: D. 1 : 1.5 Mo/L Option-IV Mo/L Mo/L Mo a /L Mo (a/L-1) Option-I Option-II Mo L a A B Mo/L Option-III ܮ ܮ/2 ܣ ܤ ܥ + Sign convention of shear force for all options (+) (+) (-) (+) (-) (+)
Year: 2018 | Type: NAT | Marks: 2
A circular steel bar of diameter 10 mm is bent into the shape as shown in figure, and lies in x-z plane. A horizontal force P is applied along the positive z-direction as shown. The yield strength of the steel is 200 MPa. Neglecting the effect of transverse shear, the load P (in Newton) required to initiate yielding as per maximum shear stress theory of failure is…………[up to two decimal places]
Answer: 195.00 to 197.00
Year: 2018 | Type: NAT | Marks: 2
Two sliders A and B, connected by a rigid link of length L, slide in two mutually perpendicular and frictionless guide-ways. At a particular instance, the slider A is moving in the downward direction with a speed of 0.05 m/s. At this instance, the magnitude of the velocity of slider B (in m/s) is ……[up to two decimal places]
Answer: 0.01 to 0.02
Year: 2018 | Type: NAT | Marks: 2
A simply supported beam ABC is subjected to load as shown in the figure. The 20 kN load is applied at point B with the help of a welded bracket as shown. The beam has a rectangular cross-section of 15 mm width and 100 mm depth as shown. The maximum transverse shear stress developed in the beam (in MPa) is ……..[up to one decimal place] ݖ ݕ 100 50 ݔ Enlarged view of the cross-section 1 m 20݇N ܣ ܤ ܥ 1 m 0.25 m 5݇N/m 0.5 m 0.5 m 100 mm 15 mm
Answer: 14.5 to 15.5
Year: 2018 | Type: NAT | Marks: 2
A rigid rod ABC, in the form of a quarter-circular arc of radius R, is hinged at C and supported by a roller at B. A vertical force P is applied at the end A of the bar. For the reactions at B and C to be equal in magnitude, the value of the angle θ (in degrees) is ………. [up to two decimal places].
Answer: 26.00 to 27.00
Year: 2018 | Type: NAT | Marks: 2
A marble of mass m slides along a frictionless linear slide AB kept in a vertical plane. The marble is released from point A with zero initial velocity, and it reaches point B under the action of gravity. Assuming the acceleration due to gravity to be 9.81 m/s2, the speed (in m/s) of the marble when it just reaches point B is………[up to two decimal places].
Answer: 3.10 to 3.20
Year: 2018 | Type: NAT | Marks: 2
A horizontal force 10 N is applied at support B on the frame as shown in figure. Considering only bending deformation, the vertical reaction (in N) at support B is ………. [up to one decimal place] ܴ ܣ ܤ 10 N
Answer: 13.5 to 14.5
Year: 2017 | Type: NAT | Marks: 1
GATE XE 2017, Solid Mechanics, Q.1: see the question image.
Answer: 69 to 73
Year: 2017 | Marks: 1
GATE XE 2017, Solid Mechanics, Q.2: see the question image.
Answer: B.
Year: 2017 | Marks: 1
GATE XE 2017, Solid Mechanics, Q.3: see the question image.
Answer: C.
Year: 2017 | Marks: 1
GATE XE 2017, Solid Mechanics, Q.4: see the question image.
Answer: C.
Year: 2017 | Marks: 1
GATE XE 2017, Solid Mechanics, Q.5: see the question image.
Answer: A.
Year: 2017 | Marks: 1
GATE XE 2017, Solid Mechanics, Q.6: see the question image.
Answer: B.
Year: 2017 | Marks: 1
GATE XE 2017, Solid Mechanics, Q.7: see the question image.
Answer: A.
Year: 2017 | Type: NAT | Marks: 1
GATE XE 2017, Solid Mechanics, Q.8: see the question image.
Answer: 0.26 to 0.28
Year: 2017 | Marks: 1
GATE XE 2017, Solid Mechanics, Q.9: see the question image.
Answer: A.
Year: 2017 | Marks: 2
GATE XE 2017, Solid Mechanics, Q.10: see the question image.
Answer: D.
Year: 2017 | Type: NAT | Marks: 2
GATE XE 2017, Solid Mechanics, Q.11: see the question image.
Answer: 134 to 136
Year: 2017 | Type: NAT | Marks: 2
GATE XE 2017, Solid Mechanics, Q.12: see the question image.
Answer: 0.55 to 0.65
Year: 2017 | Type: NAT | Marks: 2
GATE XE 2017, Solid Mechanics, Q.13: see the question image.
Answer: 1785 to 1792
Year: 2017 | Type: NAT | Marks: 2
GATE XE 2017, Solid Mechanics, Q.14: see the question image.
Answer: 0.45 to 0.50
Year: 2017 | Type: NAT | Marks: 2
GATE XE 2017, Solid Mechanics, Q.15: see the question image.
Answer: 32 to 35
Year: 2017 | Type: NAT | Marks: 2
GATE XE 2017, Solid Mechanics, Q.16: see the question image.
Answer: 10
Year: 2017 | Type: NAT | Marks: 2
GATE XE 2017, Solid Mechanics, Q.17: see the question image.
Answer: 2
Year: 2017 | Marks: 2
GATE XE 2017, Solid Mechanics, Q.18: see the question image.
Answer: A.
Year: 2017 | Type: NAT | Marks: 2
GATE XE 2017, Solid Mechanics, Q.19: see the question image.
Answer: 17 to 18
Year: 2017 | Marks: 2
GATE XE 2017, Solid Mechanics, Q.20: see the question image.
Answer: C.
Year: 2017 | Marks: 2
GATE XE 2017, Solid Mechanics, Q.21: see the question image.
Answer: B.
Year: 2017 | Marks: 2
GATE XE 2017, Solid Mechanics, Q.22: see the question image.
Answer: B.
Year: 2016 | Marks: 1
A single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping coefficient of 100 N-s/m. To make the system critically damped
Answer: D. no change in any of the system parameters is required.
Year: 2016 | Marks: 1
A “L” shaped robotic arm AB is connected to a motor at end A and a magnetic gripper at B as shown in the figure. If the arm is rotating with an angular velocity of 2 rad/s and an angular acceleration of 3 rad/s2, the magnitude of the acceleration (in m/s2) of the end B is
Answer: B. 2.5
Year: 2016 | Type: NAT | Marks: 1
A block of weight 100 N is in static equilibrium on an inclined plane which makes an angle 15º with the horizontal. The coefficient of friction between the inclined plane and the block is 0.3. The magnitude of friction force (in N) acting on the block is __________ 0.3 m 0.4 m A B 900 2 rad/s 3 rad/s2 15º 100 N
Answer: 25.5 to 26.0
Year: 2016 | Marks: 1
The lower end A of the rigid bar AB is moving horizontally on the floor towards right with a constant velocity of 5 m/s and the point B is sliding down the wall. The magnitude of the velocity of point B at the instant θ=30º is
Answer: D. 8.66 m/s
Year: 2016 | Type: NAT | Marks: 1
The state of plane stress at a point in a body is shown in the figure. The allowable shear stress of the material of the body is 200 MPa. According to the maximum shear stress theory of failure the maximum permissible value of σ (in MPa) is __________
Answer: 200
Year: 2016 | Marks: 1
For a slender steel column of circular cross-section the critical buckling load is cr P . If the diameter of the column is doubled (keeping other material and geometrical parameters same), then the critical buckling load of the column is
Answer: D. 16 cr P
Year: 2016 | Type: NAT | Marks: 1
A closed thin cylindrical pressure vessel having an internal diameter of 1000 mm and a thickness of 10 mm is subjected to an internal pressure of 4 MPa. The maximum shear stress (in MPa) induced in the cylinder is __________ (neglect the radial stress).
Answer: 100
Year: 2016 | Type: NAT | Marks: 1
A solid circular shaft subjected to pure torsion develops a maximum torsional shear stress of 120MPa. Keeping the torsional moment same, if the diameter of the shaft is doubled then the maximum shear stress (in MPa) induced in the shaft is __________ A B θ Floor Wall
Answer: 15
Year: 2016 | Type: NAT | Marks: 1
On a single straight track, a vehicle of mass 500 kg moving with a velocity of 25 m/s strikes another vehicle of mass 250 kg moving with a velocity 10 m/s in the same direction. After the impact, if both the vehicles stick together, the common velocity (in m/s) with which both the vehicles will move together is __________
Answer: 20
Year: 2016 | Type: NAT | Marks: 2
A system with three forces and a concentrated moment at A is shown in the figure. The system is replaced by an equivalent force system with a single force and a single couple at point ‘O’. The magnitude (in N-m) of the equivalent couple at ‘O’ is __________
Answer: 150
Year: 2016 | Type: NAT | Marks: 2
A block A on a smooth inclined plane is connected to block B as shown in the figure using an inextensible cord which pass over a mass-less and friction-less pulley. Initially, the block B is constrained to be at rest. If the constraint on block B is released, the magnitude of velocity (in m/s) of the block ‘B’ after 2 seconds from its release is __________ (assume g =10 m/s2). 200 N 30o O 100 N 50 N-m 2 m 2 m 50 N 4 m A 1 m A B 30º 10 kg 5 kg
Answer: 10
Year: 2016 | Marks: 2
The vibrating system shown in the figure carries a mass of 10 kg at the free end, where the static deflection is 1 mm. This system is to be replaced by an equivalent vibrating spring mass system having equivalent mass of 2 kg (assume g =10 m/s2). The natural frequency (in rad/s) and the stiffness (in kN/m) of the equivalent system respectively are
Answer: C. 100 and 20
Year: 2016 | Marks: 2
A beam having flexural rigidity EI and length L is subjected to a concentrated end moment 0 M as shown in the figure. For 3 2 4 10 N-m EI =× , 1m L = and 0 8kN-m M = , the strain energy stored (in kN-m) in the beam and the rotation (in rad) at the free end respectively are
Answer: B. 8.00 and 2.00
Year: 2016 | Marks: 2
At a point ‘O’ on a metal sheet a square OABC of a unit side length is drawn. The square undergoes a small uniform elastic deformation and deforms to OA*B*C* (dashed lines) as shown in the figure. All dimensions are in mm and the figure is not to scale. The normal strains xε, y ε and shear strain xy γ developed in the square respectively are
Answer: D. 0.0020, 0.0025 and 0.0020 − −
Year: 2016 | Marks: 2
Mohr’s circle for the state of plane stress at a point is shown in the figure. Unit of stress is MPa and the circle is drawn not to scale. Which one of the following options (stress values in MPa) is true? (normal stress) (shear stress) A B C O O – Origin of – axis C – Center of Mohr’s circle 20 30 40 ( A, A) ( , ) ( , 0) ( , 0)
Answer: A. 1 2 50, 10, 30, 70 A B σ σ σ σ =− = = =−
Year: 2016 | Type: NAT | Marks: 2
As shown in the figure, links AB and CD support the rigid member BD. Links AB and CD are made of aluminum alloy( ) 100GPa E = and each has a cross-sectional area of 2 100mm . All the members are pin connected and all the dimensions are in mm. Neglecting the weights of the members, the elongation (in mm) of the link AB is __________ A B C D 6 kN 400 400 100 200
Answer: 0.16
Year: 2016 | Type: NAT | Marks: 2
Figure shows an elastic beam of constant flexural rigidity EI and length . L The transverse deflection ( ) v x for the beam is represented by the equation ( ) 3 2 0 ( ) (4 ), v x M x x L EI L = − where 0 M is the applied couple. If 100mm L = and 0 100 N-mm M = , then the magnitude of the shear force (in N) at the middle of the beam (at / 2) x L = is __________
Answer: 1.5
Year: 2016 | Marks: 2
Which one of the following represents the correct bending moment diagram of the beam PQR loaded as shown in the figure?
Answer: B.
Year: 2016 | Marks: 2
A point in a body is subjected to plane state of stress in XY plane. If 140MPa, x σ= 60MPa y σ = and the major principal stress is 150 MPa, the magnitude of the in-plane shear stress xy τ (in MPa) is
Answer: B. 30
Year: 2016 | Type: NAT | Marks: 2
A 40 mm diameter rotor shaft of a helicopter transmits a torque T = 0.16 π kN-m and a tensile force P = 24 π kN. The maximum tensile stress (in MPa) induced in the shaft is __________. Use the value of π = 3.1416. T T P P
Answer: 80
Year: 2016 | Type: NAT | Marks: 2
A wooden block of length 400 mm, width 50 mm and depth 100 mm is subjected to uniaxial load as shown in the figure. An inclined plane ABCD is shown which makes an angle θ with the XZ plane and the line CD is parallel to the Z-axis. The normal stress on the plane ABCD is 1 n σ when o θ 30 = and the normal stress on the plane ABCD is 2 n σ when o 120 θ= . The value of 2 1 n n σ σ is __________ 10 kN X 10 kN θ A C D B Y Z 400 mm
Answer: 3
Year: 2016 | Marks: 2
For the truss shown in the figure, which one of the following statements is true?
Answer: C. AG, BH and HF are zero force members.
Year: 2015 | Type: NAT | Marks: 1
GATE XE 2015, Solid Mechanics, Q.1: see the question image.
Answer: 0
Year: 2015 | Marks: 1
GATE XE 2015, Solid Mechanics, Q.2: see the question image.
Answer: D.
Year: 2015 | Type: NAT | Marks: 1
GATE XE 2015, Solid Mechanics, Q.3: see the question image.
Answer: 1.9 to 2.1
Year: 2015 | Marks: 1
GATE XE 2015, Solid Mechanics, Q.4: see the question image.
Answer: A.
Year: 2015 | Marks: 1
GATE XE 2015, Solid Mechanics, Q.5: see the question image.
Answer: B.
Year: 2015 | Type: NAT | Marks: 1
GATE XE 2015, Solid Mechanics, Q.6: see the question image.
Answer: 4
Year: 2015 | Marks: 1
GATE XE 2015, Solid Mechanics, Q.7: see the question image.
Answer: A.
Year: 2015 | Type: NAT | Marks: 1
GATE XE 2015, Solid Mechanics, Q.8: see the question image.
Answer: 0.14 to 0.16
Year: 2015 | Marks: 1
GATE XE 2015, Solid Mechanics, Q.9: see the question image.
Answer: A.
Year: 2015 | Type: NAT | Marks: 2
GATE XE 2015, Solid Mechanics, Q.10: see the question image.
Answer: 4
Year: 2015 | Marks: 2
GATE XE 2015, Solid Mechanics, Q.11: see the question image.
Answer: D.
Year: 2015 | Marks: 2
GATE XE 2015, Solid Mechanics, Q.12: see the question image.
Answer: B.
Year: 2015 | Marks: 2
GATE XE 2015, Solid Mechanics, Q.13: see the question image.
Answer: C.
Year: 2015 | Type: NAT | Marks: 2
GATE XE 2015, Solid Mechanics, Q.14: see the question image.
Answer: 2.3 to 2.4
Year: 2015 | Type: NAT | Marks: 2
GATE XE 2015, Solid Mechanics, Q.15: see the question image.
Answer: 0.5
Year: 2015 | Type: NAT | Marks: 2
GATE XE 2015, Solid Mechanics, Q.16: see the question image.
Answer: 74 to 76
Year: 2015 | Marks: 2
GATE XE 2015, Solid Mechanics, Q.17: see the question image.
Answer: C.
Year: 2015 | Type: NAT | Marks: 2
GATE XE 2015, Solid Mechanics, Q.18: see the question image.
Answer: 25
Year: 2015 | Type: NAT | Marks: 2
GATE XE 2015, Solid Mechanics, Q.19: see the question image.
Answer: 5.2 to 5.4
Year: 2015 | Type: NAT | Marks: 2
GATE XE 2015, Solid Mechanics, Q.20: see the question image.
Answer: 1.3 to 1.45
Year: 2015 | Marks: 2
GATE XE 2015, Solid Mechanics, Q.21: see the question image.
Answer: A.
Year: 2015 | Type: NAT | Marks: 2
GATE XE 2015, Solid Mechanics, Q.22: see the question image.
Answer: 5
Year: 2014 | Type: NAT | Marks: 1
A steel wire of diameter 5 mm is bent around a cylindrical drum of radius 0.5 m. The steel wire has modulus of elasticity of 200 GPa. Find the bending moment in the wire in N-m.
Answer: 12.20 to 12.22
Year: 2014 | Type: NAT | Marks: 1
A compressed air tank having an inner diameter of 480 mm and a wall thickness of 8 mm is formed by welding two steel hemispheres. If the allowable shear stress in the steel is 40 MPa, find the maximum permissible pressure (in MPa) inside the tank.
Answer: 5.3 to 5.4
Year: 2014 | Marks: 1
A point in a body is subjected to a bi-axial state of stress, equal in magnitude but opposite in nature. On a plane inclined at an angle 45° with respect to x-axis (passing through the point), the
Answer: C. shear stress is maximum and normal stress is zero
Year: 2014 | Marks: 1
The Euler’s buckling load of a column fixed at both the ends is P. If one of the ends is made free, the buckling load shall change to
Answer: A. P/16
Year: 2014 | Type: NAT | Marks: 1
For the pin jointed truss, find the axial force (in kN) in the member 2-5.
Answer: 0
Year: 2014 | Marks: 1
A weightless beam subjected to two point loads is shown in the figure below. The shear force diagram of the beam is
Answer: C.
Year: 2014 | Marks: 1
The supporting structure of a water tank is made of reinforced concrete (RC) with a tubular cross section of inner diameter di, outer diameter do, height l, and Young’s modulus E. The mass of the tank is m. If mass of the supporting structure is neglected, then the natural frequency of the water tank in transverse direction is
Answer: A. ට3𝜋𝜋𝜋𝜋൫𝑑𝑑𝑜𝑜 − 4 𝑑𝑑𝑖𝑖 4൯ 64𝑙𝑙3𝑚𝑚
Year: 2014 | Marks: 1
A mass is attached to a spring and placed horizontally in a frictionless surface. A simple pendulum has been pivoted to the mass. The degree of freedom of this system is
Answer: B. 2
Year: 2014 | Marks: 1
Consider the following two statements Statement 1: A body of weight W falls from a height h and strikes the ground. If the body starts from rest, the velocity with which it strikes the ground is ඥ2𝑔𝑔ℎ , where g is the acceleration due to gravity. Statement 2: If the same body (initially at rest) slides without friction along an inclined plane PQ (angle of inclination α) starting from an elevation h above point Q, then its velocity at point Q is ඥ2𝑔𝑔ℎ The correct option is
Answer: A. Both statements 1 and 2 are true
Year: 2014 | Type: NAT | Marks: 2
A composite bar of length ‘L’ is made of a centrally placed steel plate (50 mm wide x 10 mm thick) with two copper plates (each 30 mm wide x 5 mm thick) connected rigidly on each side. If the temperature of the composite bar is raised by 50°C, find the stress developed in each copper plate in MPa. (For Steel: Es = 2x105 MPa and αs= 12x10-6 /°C; For Copper: Ec = 1x105 MPa and αc= 17x10-6 /°C)
Answer: 19.1 to 19.3
Year: 2014 | Marks: 2
The vertical deflection at the free end of the cantilever beam as shown in figure is
Answer: B. 1400/3EI
Year: 2014 | Type: NAT | Marks: 2
A hollow shaft and a solid shaft have the same length and the same outer radius R. The inner radius of the hollow shaft is 0.6 R. Assuming that both the shafts are made of same material and are subjected to the same torque, find the ratio of shear stress in hollow shaft to that in solid shaft.
Answer: 1.14 to 1.16
Year: 2014 | Marks: 2
A beam with overhangs carries one point load acting downwards and the other upward. The clockwise moment Pb is applied at each support. The bending moment at the midpoint of the beam is
Answer: A. 0
Year: 2014 | Marks: 2
A cantilever beam of length L supports a concentrated load P at the free end. The cross section of the beam is rectangular with constant width b and varying depth h. The depth h of this idealized cantilever beam varies in such a way that the maximum normal stress at every cross section remains equal to the allowable bending stress. Considering only the bending stresses, the depth hx of the fully stressed beam at any distance x from the free end shall vary
Answer: B. with square root of x
Year: 2014 | Marks: 2
A cantilever beam is subjected to following three different loading conditions: (a) a concentrated load P at its free end, (b) a couple Mo at its free end and (c) both loads acting simultaneously (a) (b) (c) The flexural rigidity of the beam may be assumed as EI. The strain energy due to bending when both loads act simultaneously
Answer: C. cannot be determined by applying the principle of superposition and the strain energy is 𝑃𝑃2𝐿𝐿3 6𝐸𝐸𝐸𝐸+ 𝑀𝑀𝑜𝑜2𝐿𝐿 2𝐸𝐸𝐸𝐸+ 𝑃𝑃𝑀𝑀𝑜𝑜 𝐿𝐿2 2𝐸𝐸𝐸𝐸
Year: 2014 | Marks: 2
A tapered rod has diameter d1 at one end which reduces uniformly to a diameter d2 over the length (L). If the modulus of elasticity of the material is E, the change in the length of the rod due to the application of axial force (P) is
Answer: A. 4𝑃𝑃𝑃𝑃 𝜋𝜋𝜋𝜋𝑑𝑑1𝑑𝑑2
Year: 2014 | Type: NAT | Marks: 2
For a point in a body subjected to a plane stress condition (σx= 100 MPa, σy= 50 MPa and τxy = τyx = 25 MPa), the maximum principal stress in MPa is_____________
Answer: 110.3 to 110.5
Year: 2014 | Marks: 2
An isotropic body is subjected to a state of stress given by: σx= 10 MPa and τxy = τyx = −20 MPa. Assuming G = 0.4E, the volumetric strain is
Answer: A. 5/E
Year: 2014 | Marks: 2
A block of weight Q rests on an inclined plane and it is attached to a string which runs over a frictionless pulley to carry a block of weight P at its other end. The coefficient of friction between the block of weight Q and the inclined plane is µ. Consider the following cases: Case I: weight Q starts moving down the inclined plane Case II: weight P starts falling down The limiting values of ratio P/Q for Case I and Case II respectively are
Answer: A. (sin 𝛼𝛼−𝜇𝜇cos𝛼𝛼) and (sin𝛼𝛼+ 𝜇𝜇cos 𝛼𝛼)
Year: 2014 | Marks: 2
To unload an item from a truck a crane boom is raised with a constant angular velocity of 1 rad/s relative to the cab and then the cab is rotated about a vertical axis with constant angular velocity of 0.5 rad/s. If the length of the boom (OP) is 10 m, the velocity of the tip (P) of the boom in m/s is
Answer: D. 5 √2 ൫−𝑖𝑖 ො−2 𝑗𝑗̂ + 2𝑘𝑘൯
Year: 2014 | Marks: 2
A block of mass 5 kg moves up on a smooth inclined plane with a velocity of 10 m/s in the direction shown. A bullet of mass 60 g travelling at 500 m/s strikes the block centrally and gets embedded in it. The velocity of the block and embedded bullet in m/s immediately after the impact is
Answer: B. 13.84 at 51.78°
Year: 2014 | Type: NAT | Marks: 2
A balloon with ballast (weight) inside it has a gross weight of 500 N. It is falling vertically with a constant acceleration of 2 m/s2. If air resistance is negligible, find the weight of ballast (in N) that must be thrown out in order to give the balloon an upward acceleration of 2 m/s2. (Acceleration due to gravity, g = 9.81 m/s2) 500 N XE (GATE 2014)
Answer: 169.3 to 169.4
Year: 2013 | Type: NAT | Marks: 1
At a point in a body subjected to plane stress, the state of stress is as shown in the Figure. One of the principal stresses is 180 MPa. Find the unknown shear stress τ (in MPa). __________
Year: 2013 | Type: NAT | Marks: 1
A point in a body is subjected to a hydrostatic pressure of 100 MPa. Find the maximum shear stress at this point in MPa. ___________
Year: 2013 | Type: NAT | Marks: 1
A circular shaft of diameter 10 mm and length 3m is subjected to a torque of T = π N-m at a location 2m away from the fixed end as shown in the Figure. Find out the angle of twist (in radians) at the free end. Shear modulus of the material of the shaft is 10 GPa. ___________
Year: 2013 | Marks: 1
A rigid massless rod ABC is hinged at A and carries a point mass M (in kg) at C. Point B is connected to a linear spring with spring constant k (in N/m) as shown in the figure. The length AB and AC area and L, respectively. Neglecting the effect of gravity, the natural frequency of this spring-mass system in rad/s is
Year: 2013 | Type: NAT | Marks: 1
A two bar truss is shown in the Figure. The cross-sectional area and Young’s modulus of bar 1 are 0.02 m2 and 200GPa, respectively. The cross-sectional area and Young’s modulus of bar 2 are 0.01 m2and 80GPa, respectively. The force F applied on the truss is 2 N. Find out the stress developed in bar 2 in Pa. ___________
Year: 2013 | Type: NAT | Marks: 1
A spring balance reads 10 kg in a lift when the lift is stationary. When the lift starts moving with a constant acceleration, the new reading is 12.3 kg. If the upward acceleration is considered positive, what is the acceleration of the lift? Acceleration due to gravity may be taken as 10 m/s2downwards.______________
Year: 2013 | Type: NAT | Marks: 1
A force F = 2 N is applied on a block of mass M = 0.5 kg as shown in the figure. The block is constrained to move along the horizontal direction in a guideway. Find out the distance (in meters) travelled by the block in 2 s starting from rest. Neglect any friction between the block and the guideway. ____________ P B A L k t Ice surface Wooden board V x y
Year: 2013 | Type: NAT | Marks: 1
A man of mass 50 kg is walking on a long wooden board of mass 200 kg (as shown in the Figure). The wooden board is initially at rest on a frictionless ice surface. If the man walks with a velocityof V =1 m/s in the positive x direction relative to the wooden board, find the velocity of the board in m/s. Velocity is positive in the positive x direction. _____________
Year: 2013 | Marks: 1
A rigid bar AB is hinged at B through a torsional spring with spring constant kt.. For small rotations of the bar AB about B, the critical load Pcr is given by
Year: 2013 | Type: NAT | Marks: 2
A disk of mass M= 14kg and radius 1 m is attached to a spring which has a stiffness k = 75 N/m and an unstretched length of 1m. If the disk is released from rest in the position shown in the Figure and the disk rolls without slipping, find its angular velocity (in rad/s) at the instant the center of mass is displaced by 3 m. ______________
Year: 2013 | Type: NAT | Marks: 2
A strain gauge is mounted on the outer surface of a thin cylindrical pressure vessel in the circumferential direction. The mean diameter and thickness of the cylinder are 4.0 m and 20 mm, respectively. Young’s modulus and Poisson’s ratio of the material of the cylinder are 200 GPa and 0.25, respectively. Find the pressure in MPa inside the cylindrical vessel when the strain gauge indicates a strain of 7.0x 10-4. ____________
Year: 2013 | Type: NAT | Marks: 2
A solid shaft of diameter 100 mm is rotating at a constant angular speed of (10/ π) rad/s. The shaft carries three rigid pulleys A, B and C as shown in the Figure. Pulley B is connected to a motor supplying 10kW power. Pulley B and C are connected to two pumps consuming 5kW each. Find the maximum shear stress (in MPa) in the shaft due to torsion alone. __________ EI L k P 40 kN 20 kN A B C D 2.5 m 2 m 3 m
Year: 2013 | Marks: 2
A beam is fixed at the left end and supported by a spring at the other end. The length of the beam is L and its flexural rigidity is EI. The spring constant of the spring is = ଷாூ య. A vertical downward load P is applied at the right end. The deflection of the point under the load P is
Year: 2013 | Type: NAT | Marks: 2
Find the maximum bending moment (magnitude wise) in kN-m for the beam shown in the Figure. ______ H 45 o S v r x Y q Arc of a circle P
Year: 2013 | Type: NAT | Marks: 2
A projectile is fired with a velocity V= 3√2 m/s from a point at height H = 0.8 m at an angle of 450 with respect to the horizontal direction as shown in the Figure. Find the horizontal distance S in meters travelled by the projectile when it hits the ground. Take acceleration due to gravity as10 m/ s2. __________
Year: 2013 | Type: NAT | Marks: 2
A particle P is moving on a circular path of radius r = 1m. The angular location θof the particle is measured as shown in the Figure. The motion of the particle is described by ߠ= 2 sin(ݐ). Find the magnitude of the total acceleration (in m/s2) of the particle at time t = π/3 seconds. _________ A B C P 900 100 MPa 40 MPa 100 MPa 40 MPa 40 MPa 40 MPa 45 o A B
Year: 2013 | Marks: 2
Neglecting the axial compression of member AB, the deflection of point C in the direction of the load is
Year: 2013 | Marks: 2
The maximum bending stress in the frame is
Year: 2013 | Marks: 2
One of the principal stresses(in MPa) is
Year: 2013 | Marks: 2
The normal stress on the plane AB (in MPa) is
Year: 2013 | Marks: 2
The stress in rod 1 (in MPa) is
Year: 2013 | Marks: 2
Considering the displacement to the right as positive, the displacement (in mm) of the interface between the two rods is
Year: 2012 | Marks: 1
The axial force diagram for the weightless beam subjected to the inclined force P = 5 kN is
Answer: A.
Year: 2012 | Marks: 1
A block of weight W, connected to two springs with spring constants 1k and 2k , rests initially on a horizontal frictional surface. The coefficient of static friction between the block and the surface is μ. Both springs are initially undeformed. The magnitude of force F, applied to the second spring, is now gradually increased. The block will start to slide when F becomes
Answer: A. W μ
Year: 2012 | Marks: 1
Three connected railway coaches A, B and C of masses A m , B m and C m , respectively are being pulled by a locomotive with force F over a horizontal track. The coaches may be assumed to move on frictionless wheels with negligible air resistance. The tension in the connector between coaches A and B is
Answer: D. ( )/( ) B C A B C F m m m m m + + +
Year: 2012 | Marks: 1
For the beam-column configurations shown in figure, the minimum Euler buckling load is obtained for the case (Young’s modulus and second moment of cross-sectional area are as indicated)
Answer: C. (iii)
Year: 2012 | Marks: 1
A disk of mass g 25 .0 = m and radius mm 10 = r is at rest relative to a mass-less horizontal turntable spinning about a vertical axis at an angular speed of s/ rad 2 = ω . The turntable is assumed to be mounted on frictionless bearings. Another identical, initially non-rotating disk is dropped onto the spinning disk. Friction causes both disks (and the turntable) to eventually rotate at the same angular speed. The eventual angular speed of the disks is
Answer: B. 1 rad/s
Year: 2012 | Marks: 1
A rocket in the atmosphere is accelerating upwards with acceleration a m/s2. The natural frequency of a spring-mass system (with mass m kg and spring constant k N/m), suspended vertically inside the rocket, is (take g m/s2 to be the acceleration due to gravity)
Answer: B. k m
Year: 2012 | Marks: 1
An irregular planar body in space is acted upon by a force (2 ) F i j N = + at position 1 ( 2 ) r i j m = + and a moment 3 M kNm = at position 2 ( 2 ) r i m =− . The corresponding equivalent force O F and moment O M at the origin are
Answer: B. (2 ) ; 0 O O F i j N M Nm = + =
Year: 2012 | Marks: 1
A hollow shaft and a solid shaft constructed of the same material have the same length and the same outer radius R. The inner radius of the hollow shaft is 0.6 R. Assuming that both shafts are subjected to the same torque, the ratio of the maximum shear stress in the hollow shaft to that in the solid shaft is
Answer: C. 1.15
Year: 2012 | Marks: 1
A point in a beam experiences a tensile stress (due to bending) of 50 N/mm2 and a shear stress of 20 N/mm2. The principal stresses are
Answer: C. 57 N/mm2 tension, 7 N/mm2 compression
Year: 2012 | Marks: 2
Consider a simply supported beam loaded either by a uniformly distributed transverse load or by a concentrated transverse load applied at the center such that the maximum bending stress in both cases is the same. The ratio of the strain energy for the two cases is
Answer: C. 8/5
Year: 2012 | Marks: 2
A small railway bridge is constructed from identical steel truss members, each of length l , cross- sectional area A and Young’s modulus E . A train stops on the bridge. The loads applied by the train on the truss on one side of the bridge may be assumed to act at pins A, B and C, as shown. The displacement of the support C due to this loading is
Answer: D. /( 3 ) Ql AE
Year: 2012 | Marks: 2
A vertical pole, cantilevered at the bottom, has a solid circular cross-section of diameter d = 49.21 mm. It is loaded by a horizontal force P = 6675 N at the top end. The maximum shear stress in the pole is
Answer: C. 4.68 N/mm2
Year: 2012 | Marks: 2
A striker with mass m=20 kg is attached to the end of a mass-less rigid bar of length R=0.3m. The bar is hinged to support A, and swings down from an initial horizontal position such that the striker hits mass M= 5kg elastically. The mass M slides (in a straight line) along the table, from point B towards the spring located at point C, 0.2 m away from B. Assume that the coefficient of friction in the region BC is 0.4 d μ= ; the region CD frictionless. Let the spring constant of the spring be k = 4000 N/m. If the striker rises to a maximum height of 0.1m below its starting location, then the maximum compression of the spring is (let acceleration due to gravity g = 10 m/s2, the dimensions of the striker and mass are small)
Year: 2012 | Marks: 2
A cube, made of aluminum, of dimension 0.1 m × 0.1 m × 0.1 m, rests against a rigid wall (with normal in the y-direction), as shown in the figure. Another parallel rigid wall is located at a clearance of 0.2 mm from the block. Assuming all contacts to be frictionless, if the block is heated by 150 = ΔT °C, the normal stress yy σ induced in the block is (for aluminum GPa 70 = E ; 3.0 = ν ; / 10 20 6 − × = α °C)
Answer: C. MPa 70 − = yy σ
Year: 2012 | Marks: 2
A thin walled spherical pressure vessel made of a linear elastic isotropic material has inner radius r and thickness t before pressurization. When subjected to internal pressure p , elements of the pressure vessel wall experience a state of stress described by a single point ( , ) ( /(2 ),0) pr t στ= in Mohr’s circle. The reduction of the wall thickness due to pressurization
Year: 2012 | Marks: 2
For small oscillations, the natural frequency of the system in terms of K, a , b and M is (assuming ideal joints and mass-less rigid rod ABC)
Answer: D. 2 2 Ka Mb
Year: 2012 | Marks: 2
For an internal pressure of 800 kPa the maximum shear stress for the cylindrical part of the vessel is
Year: 2012 | Marks: 2
At which of the following internal pressures will the cylindrical vessel yield as per the Tresca criterion if the yield strength of the material in tension is 320 MPa
Answer: A. 3.55 MPa
Year: 2012 | Marks: 2
The maximum bending stress in the beam is
Answer: B. 64 MN/m2
Year: 2012 | Marks: 2
The vertical deflection at the ends is
Year: 2012 | Marks: 2
If the deflection at the free-end (under load P, with end moment M=0) is measured as δ = 5 mm, the flexural rigidity EI for the beam is (in N m2)
Answer: B. 66,000
Year: 2012 | Marks: 2
The value of the additional end moment M (in N.m) required to obtain an upward deflection of 1 mm at the free end, is (moment is positive in counterclockwise direction)
Answer: A. 533.33 −
Year: 2007 | Marks: 1
A simply supported beam AB is subjected to a horizontal force, $P$, as shown in the figure. Shear force at section $a$-$a$ is given by
Year: 2007 | Marks: 1
The two-dimensional state of stress at a point is given by the figure (10 MPa biaxial tension in $x$ and $y$). The corresponding Mohr's circle is
Year: 2007 | Marks: 1
The kind of fracture surface observed in a brittle specimen that fails under a uniaxial tensile test is
Year: 2007 | Marks: 1
Two masses are attached to the two ends of a cable which passes over two frictionless pulleys as shown in the figure. (acceleration due to gravity $= g$). The acceleration of the $100\text{ kg}$ mass is
Year: 2007 | Marks: 1
A block of mass $m$ is released at rest from a point P of a rough circular path of radius $r$ as shown in the figure. There is a spring of stiffness $k$ at the other end of the path. (acceleration due to gravity $= g$). The maximum spring deflection is
Year: 2007 | Marks: 1
The truss shown in the figure is
Year: 2007 | Marks: 2
A mass $m_1$ with velocity $v_1$ impacts with a mass $m_2$ at rest. After the impact, the mass $m_1$ comes to rest. Then the coefficient of restitution $e$ should be
Year: 2007 | Marks: 2
A beam ABCD with simple supports at A, B and D and an internal hinge at C is subjected to loads as shown in the figure. The reaction at middle support is given by
Year: 2007 | Marks: 2
A bar of cross sectional area, $A$, is loaded as shown in the figure. The normal stress on a section $a$-$a$ inclined at $45^\circ$ to the axis of the bar is
Year: 2007 | Marks: 2
In a two-dimensional state of stress at a point, the maximum shear strain is found to be $\gamma_{\max} = 500\text{ }\mu\text{m/m}$. The sum of the normal stresses on two perpendicular planes at that point is $40\text{ MPa}$. (Young's Modulus $E = 200\text{ GPa}$; Modulus of rigidity $G = 80\text{ GPa}$; Poisson's ratio $\nu = 0.25$). The principal stresses at the point are
Year: 2007 | Marks: 2
A mass of $2\text{ kg}$ is hung by a string of length $1.5\text{ m}$ as shown in the figure. The mass revolves in a horizontal circular path at $50$ revolutions per minute. The tension in the string in Newtons is
Year: 2007 | Marks: 2
A simply supported beam of span $L$ is subjected to a concentrated load $P$ at midspan. The cross-section of the beam is rectangular. The ratio of the shear stress at $1/4\text{th}$ the depth of the beam to the shear stress at the center of the cross-section is
Year: 2007 | Marks: 2
An L-shaped bar of square cross-section with sides, $b$, is loaded as shown in the figure. If the value of the stress component $\sigma_{xx}$ at point P is zero, the distance $a$ of the force $F$ from the $x$-axis should be
Year: 2007 | Marks: 2
The rigid links PQ and PR of length $L$ each are connected to 3 sliders P, Q and R, by pin-joints as shown in the figure. The sliders, Q, and R, slide in the $y$-direction while the slider, P, slides in the $x$-direction. When the slider, P, is at the position $x = 40\text{ mm}$, its velocity is $30\text{ mm/s}$ along the positive $x$-direction. At that instant, the velocity of slider, Q, will be ($L = 50\text{ mm}$)
Year: 2007 | Marks: 2
An open ended thin-walled straight pipe is made of a material that can carry a maximum shear stress of $\tau_{\max}$. The pipe is of diameter, $d$, and thickness, $t$. The maximum internal pressure allowable is given by (neglecting the normal stress in the radial direction)
Year: 2007 | Marks: 2
A stepped shaft PQR is fixed at both the ends as shown in the figure. A torque $T$ is applied at point Q. The polar moments of inertia of the shafts PQ and QR are $J_1$ and $J_2$ respectively. $G$ is the modulus of rigidity. The angle of twist at point Q due to torque, $T$, is given by (in radians)
Year: 2007 | Marks: 2
Group I contains beams with different types of supports and loading conditions (P: Simply supported beam with central point load $F$; Q: Simply supported beam with UDL $w=F/L$; R: Cantilever beam with tip point load $F$; S: Cantilever beam with UDL $w=F/L$). The beams have the same flexural rigidity $EI$ and span $L$. Group II contains the maximum deflections: (1) $\frac{1}{3}\left(\frac{FL^3}{EI}\right)$, (2) $\frac{1}{8}\left(\frac{FL^3}{EI}\right)$, (3) $\frac{1}{48}\left(\frac{FL^3}{EI}\right)$, (4) $\frac{5}{384}\left(\frac{FL^3}{EI}\right)$. Match the beam from Group I with the maximum deflection given in Group II.
Year: 2007 | Marks: 2
Two bars of different Young's moduli, $E_1$ and $E_2$, but with the same cross sectional area, $A$, and coefficient of thermal expansion, $\alpha$, are attached together at one end and fixed at the other as shown in the figure. The construction of this setup was carried out at an ambient temperature of $25^\circ\text{C}$. The stress in the bars when the temperature is uniformly increased by $10^\circ\text{C}$ is
Year: 2007 | Marks: 2
A cylinder of radius $r$ and mass $m$ is placed with no initial velocity on a conveyor belt as shown in the figure. There is a frictional contact between the cylinder and the belt at B. A vertical stopper with a smooth surface prevents the cylinder from rolling away. ($I$ is the moment of inertia of the cylinder; $\alpha$ is the angular acceleration of the cylinder; $\mu$ is the coefficient of friction between the cylinder and the belt and, $g$, is the acceleration due to gravity). The valid free-body diagram of the cylinder just after placing it on the belt (that shows inertial forces also) is
Year: 2007 | Marks: 2
The figure below shows 4 long columns with different support conditions but the same flexural rigidity $EI$. Let P, Q, R, and S be the values of their critical buckling load as shown below the respective columns. P, Q, R and S can be arranged in increasing order as
Year: 2007 | Marks: 2
A circular shaft of diameter, $d$, is fixed at one end and subjected to an axial force, $P$, and a torque, $T$, at the other end. The torque, $T$, is equal to $Pd/8$. The tensile yield stress of the shaft material is $\sigma_y$. A point on the surface of the shaft will yield according to the Tresca yield criterion if $P$ is equal to
Year: 2007 | Marks: 2
A single degree freedom system consisting of 2 springs and a mass is shown in the figure. The natural frequency of the system in radians/sec is given by
Year: 2007 | Marks: 2
Common Data: For the truss shown in the figure, both the members have a cross sectional area $A$ and Young's modulus $E$. The vertical deflection at point Q is
Year: 2007 | Marks: 2
Common Data: For the truss shown in the figure, both the members have a cross sectional area $A$ and Young's modulus $E$. The horizontal deflection at point Q is
Year: 2007 | Marks: 2
Linked Answer Q.25 & Q.26: A propped cantilever beam of span $4\text{ m}$ is subjected to a uniformly distributed load of $20\text{ kN/m}$ as shown in the figure. The reaction at the roller support is
Year: 2007 | Marks: 2
Linked Answer Q.25 & Q.26: A propped cantilever beam of span $4\text{ m}$ is subjected to a uniformly distributed load of $20\text{ kN/m}$ as shown in the figure. The maximum bending moment in the beam is
Year: 2007 | Marks: 2
Linked Answer Q.27 & Q.28: A cylinder of mass, $m$, and radius, $r$, is rolling without slipping down an inclined plane that makes an angle, $\theta$, with the horizontal. The radius of gyration, $k$, of the cylinder is half the radius. (The coefficient of friction is, $\mu$; Acceleration due to gravity is, $g$). The frictional force acting on the cylinder is given by
Year: 2007 | Marks: 2
Linked Answer Q.27 & Q.28: A cylinder of mass, $m$, and radius, $r$, is rolling without slipping down an inclined plane that makes an angle, $\theta$, with the horizontal. The radius of gyration, $k$, of the cylinder is half the radius. (The coefficient of friction is, $\mu$; Acceleration due to gravity is, $g$). The angular acceleration of the cylinder is given by
