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All ISRO Mechanical & Aerospace papers
80 questions. Answers are shown only where the official answer key is available.
Topic: Thermodynamics
The pressure P of a gas in terms of its mean kinetic energy per unit volume E is equal to
Answer: D. 2E/3
Explanation: Kinetic energy for gas KE = (3/2)RT = (3/2)PV. Therefore, KE/V = (3/2)P = E, which means P = (2/3)E.
Topic: Thermodynamics
Work done in a free expansion process is
Answer: C. zero
Explanation: The work done in a free expansion process is zero because free expansion is an irreversible adiabatic and isentropic process. In free expansion, there is no external resistance upon which system can apply force.
Topic: Thermodynamics
If the value of n is infinitely large in a polytropic process PV^n=C, then the process is known as constant
Answer: A. volume
Explanation: PV^n = C can be written as P^(1/n) * V = C^(1/n). If n is infinity, then 1/n approaches 0, leaving V = Constant (C). This is a constant volume process.
Topic: Thermodynamics
During the charging of a storage battery, the current I is 20A and the voltage E in 12.8V. The ratio of heat transfer from the battery is 16W. At what rate is the internal energy increasing?
Answer: D. 240 Js^-1
Explanation: Energy stored in battery during charging = (V * I) - Q = (12.8 * 20) - 16 = 256 - 16 = 240 W (or Js^-1).
Topic: IC Engines
The compression ratio for diesel engines is close to
Answer: C. 15 to 20
Explanation: For diesel engine compression ratio rc = 15-22. For Otto engine rc = 7-12. For Dual cycle engine rc = 13-17.
Topic: Thermodynamics
One kg of carbon monoxide requires how much quantity of oxygen to produce 11/7 kg of carbon dioxide gas?
Answer: A. 4/7 kg
Explanation: CO + 0.5 O2 -> CO2. 1/2 mole of O2 would make 1 mole CO2. So, 16 kg O2 would make 44 kg CO2. Then (16/44) kg O2 would make 1 kg CO2. Therefore, 11/7 kg CO2 is made by (11/7) * (16/44) kg O2 = 4/7 kg O2.
Topic: Thermodynamics
The entropy of water at 0 K is assumed to be
Answer: D. 0
Explanation: The entropy of water at 0 K is assumed to be zero.
Topic: Thermodynamics
An expression process as per law PV = constant is known as
Answer: B. hyperbolic expansion
Explanation: We know that PV = nRT = constant. For a constant number of moles, temperature is constant. In a P-V diagram, this represents a hyperbolic curve.
Topic: Fluid Mechanics
Speed of an aeroplane is measured by
Answer: A. pitot tube
Explanation: Pitot tube is used to measure the velocity of airplanes and boats. Hot Wire Anemometer measures fluid velocity, Venturi meter measures flow rate, and Rotameter measures volumetric flow rate.
Topic: Fluid Mechanics
Euler's dimensionless number relates the following
Answer: C. pressure force and inertial force
Explanation: Euler Number (Eu) is defined as the ratio of Inertial Force to Pressure Force, i.e., $\sqrt{Fi / Fp}$.
Topic: Fluid Mechanics
Speed of sound in water is equal to (K-bulk modulus, p-density)
Answer: A. $\sqrt{K/p}$
Explanation: Speed of sound in water is C = $\sqrt{K/p}$, where K is Bulk modulus and p is Density.
Topic: Fluid Mechanics
For an irrotational flow, d²(phi)/dx² + d²(phi)/dy² = 0 is the equation given by
Answer: C. Laplace
Explanation: The expression d²(phi)/dx² + d²(phi)/dy² = 0 is known as the Laplace equation.
Topic: Thermodynamics
A simple compressible substance inside a cylinder undergoes a change of state quasistatically, isothermally and at constant pressure of 1.5 MPa. If the enthalpy change for the system is 4000 kJ at 150 °C, what is the corresponding change in its entropy?
Answer: A. 9.45 kJ K^-1
Explanation: Since it is a phase change (temperature is constant), we use dH = TdS + VdP. At constant pressure (dP = 0), dH = TdS. Entropy change dS = dH / T = 4000 / (150 + 273) = 9.45 kJ/K.
Topic: Fluid Mechanics
The velocity of sound in a gaseous medium at a temperature of 400K is 400 ms^-1. If the temperature of the medium is increased to 600 K, the velocity of sound will be nearly
Answer: B. 490 ms^-1
Explanation: Velocity of sound in a gaseous medium C = $\sqrt{gamma * R * T}$. Thus, C is proportional to $\sqrt{T}$. C2 = C1 * $\sqrt{T2/T1}$ = 400 * $\sqrt{600/400}$ = 489.89, which is approximately 490 m/s.
Topic: Fluid Mechanics
Stress strain relation of the Newtonian fluid is
Answer: B. linear
Explanation: The stress-strain relation of a Newtonian fluid is linear, meaning the shear stress is directly proportional to the rate of shear strain.
Topic: Fluid Machinery
In a centrifugal pump casing, the flow of water leaving the impeller is
Answer: B. free vortex motion
Explanation: Flow inside the impeller of centrifugal pump is forced vortex motion and the flow of water leaving the impeller is free vortex motion.
Topic: Thermodynamics
For a two stage reciprocating compressor, compression from P1 to P3 is with perfect inter cooling and no pressure losses. If compression in both the cylinders follows the same polytropic process and the atmospheric pressure is Pa, then the intermediate pressure P2 is given by
Answer: B. P2 = $\sqrt{P1 * P3}$
Explanation: For perfect inter-cooling, intermediate pressure P2 is the geometric mean of initial and final pressures: P2 = $\sqrt{P1 * P3}$.
Topic: Fluid Machinery
The degree of reaction in an axial flow compressor is defined as the ratio of static enthalpy rise in the
Answer: C. rotor to static enthalpy rise in the stage
Explanation: The degree of reaction in an axial flow compressor is defined as the ratio of static enthalpy rise in the rotor to static enthalpy rise in the stage.
Topic: Engineering Physics
The frequency of ultrasonic waves is
Answer: D. above 20000 Hz
Explanation: Range of frequency of waves: Infrasonic <= 20 Hz, Sonic 20 Hz to 20 kHz, Ultrasonic > 20 kHz.
Topic: Engineering Physics
Loudness of the sound does not change with the change in
Answer: A. frequency
Explanation: Loudness refers to how loud or soft a sound feels to a listener. The loudness of sound is determined by the intensity of the sound waves and does not change with a change in frequency.
Topic: Fluid Mechanics
If the stream function of two dimensional flow is psi = 5xy, then the velocity at a point (3, 4) is
Answer: A. 25 m/s
Explanation: Velocity in x-direction U = d(psi)/dy = 5x -> U(3,4) = 15 m/s. Velocity in y-direction V = -d(psi)/dx = -5y -> V(3,4) = -20 m/s. Resultant velocity V' = $\sqrt{U² + V²}$ = $\sqrt{15^2 + (-20}$^2) = 25 m/s.
Topic: Fluid Mechanics
A glass tube of 8 mm diameter is immersed in water. Surface tension of water is 0.0075 kg m and rise of water in the tube due to capillary effect is
Answer: B. 3.75 mm
Explanation: Rise of water in the tube due to capillary effect h = (4 * sigma * cos(theta)) / (rho * g * d). For water in glass tube theta = 0, cos(0) = 1. h = (4 * 0.0075 * 1) / (1000 * 0.008) = 0.00375 m = 3.75 mm.
Topic: Fluid Machinery
An impulse turbine produces 125 hp under a head of 25 meters. By what percentage should the speed be increased for a head of 100 metres
Answer: D. 100%
Explanation: Unit speed of turbine is N1/$\sqrt{H1}$ = N2/$\sqrt{H2}$. So, N1/$\sqrt{25}$ = N2/$\sqrt{100}$, meaning N2 = 2*N1. The speed should be increased by 100%.
Topic: Fluid Machinery
The specific speed of a centrifugal pump, delivering 1000 litres of water per second against a head of 16 metre at 800 rpm
Answer: B. 100 rpm
Explanation: Specific speed of centrifugal pump Ns = N*$\sqrt{Q}$ / H^(3/4) = 800 * $\sqrt{1000 * 10^-3}$ / 16^(3/4) = 100 rpm.
Topic: Fluid Mechanics
A pipe of 0.1 m² suddenly changes to 0.5 m² area. The quantity of water flowing in the pipe is 0.5 m³/s. Head loss due to sudden enlargement is nearly
Answer: C. 0.8 m
Explanation: V1 = Q/A1 = 0.5/0.1 = 5 m/s. V2 = Q/A2 = 0.5/0.5 = 1 m/s. Head loss due to sudden enlargement h = (V1 - V2)^2 / 2g = (5 - 1)^2 / 20 = 16 / 20 = 0.8 m.
Topic: Fluid Machinery
Efficiency of a centrifugal pump is maximum when the blades are
Answer: C. backward curved
Explanation: When the blades of a centrifugal pump are backward curved, the efficiency is maximum.
Topic: Fluid Mechanics
The hydraulic diameter, Dh of a rectangular channel with sides 'a' and 'b' is,
Answer: A. Dh = 2ab / (a+b)
Explanation: Hydraulic diameter Dh = 4 * Area / Perimeter = 4(ab) / 2(a+b) = 2ab / (a+b).
Topic: Heat Transfer
Which of the following has maximum value of thermal conductivity?
Answer: B. copper
Explanation: Copper has a thermal conductivity of ~385 W/mK, Aluminium is ~210 W/mK, Brass is ~110 W/mK, and Steel is 35-55 W/mK. Copper is the highest among the options.
Topic: Heat Transfer
A steam pipe is to be insulated by 2 insulating materials put over each other. For best results
Answer: D. unpredictable
Explanation: In case of same thickness of insulation, for better insulation K1 < K2 (better insulation over pipe). However, since the thickness of insulation is not given in the question, the result is unpredictable.
Topic: Heat Transfer
The value of Biot number is very small (<0.01) when
Answer: B. conductive resistance within the body is negligible
Explanation: The value of Biot number is very small when the conductive resistance within the body is negligible (meaning its internal conductivity approaches infinity).
Topic: Heat Transfer
The critical radius of insulation for a spherical shell is
Answer: B. 2 x thermal conductivity of insulating material / heat transfer coefficient at the outer surface
Explanation: Critical radius of insulation rc = 2K/h for a spherical shell, whereas rc = K/h for a cylindrical shell.
Topic: Heat Transfer
If the temperature of a solid surface changes from 27 °C to 81 °C, then its emissive power changes in the ratio of nearly
Answer: D. 1.94
Explanation: Emissive Power (E) is proportional to T^4. E2/E1 = (T2/T1)^4 = ((81+273)/(27+273))^4 = (354/300)^4 = 1.938, which is approximately 1.94.
Topic: Refrigeration and Air Conditioning
The heat removal rate from a refrigerated space is 7.2 kW and the power input to the compressor is 1.8 kW. The coefficient of performance (COP) of the refrigerator is
Answer: A. 4
Explanation: COP of refrigerator = Heat removed from space / Work done = 7.2 / 1.8 = 4.
Topic: Heat Transfer
For a fluid having Prandtl number equal to unity, the relation between hydrodynamic boundary layer thickness (delta_1) and thermal boundary layer thickness (delta_2) is
Answer: C. delta_1 = delta_2
Explanation: The relationship is given by Pr^(1/3) = delta_1 / delta_2. If Pr = 1, then delta_1 = delta_2.
Topic: Machine Design
Life of a ball bearing at a load of 10 kN is 24000 hours. If the load is increased to 20 kN (all other conditions are same), its life in hour is
Answer: B. 3000 h
Explanation: Life L = (C/P)^n. For ball bearing n = 3, so L is proportional to 1/P³. L2/L1 = (P1/P2)^3. L2 = 24000 * (10/20)^3 = 24000 * (1/8) = 3000 hours.
Topic: Manufacturing
The main objective of 'shot peening' is to improve which property of metal parts
Answer: A. fatigue strength
Explanation: Shot peening is a cold working process used to finish metal parts to prevent failure by improving fatigue strength.
Topic: Metrology
A hole is of dimension phi 60 (+0.015 / +0.000) and the corresponding shaft is of dimension phi 60 (+0.011 / +0.001). When they are assembled they will form a
Answer: C. transition fit
Explanation: Upper size of hole = 60.015 mm. Upper size of shaft = 60.011 mm. The upper size of the shaft is more than the lower size of the hole (60mm) but less than the upper size of the hole. So the assembled parts make a transition fit.
Topic: Manufacturing
Which of the following carbon steels is most weldable
Answer: D. 0.15% carbon steel
Explanation: Low carbon steel (0.15% carbon) is most weldable among them because they can be welded with low preheat and no post-treatment is required.
Topic: Material Science
A small percentage of boron is added to steel in order to
Answer: D. increase hardenability
Explanation: Boron gives hardness to steel. So, a small percentage of boron is added to steel in order to increase hardenability.
Topic: Strength of Materials
A material that exhibits the same elastic properties in all directions at a point is called
Answer: C. isotropic
Explanation: A material that exhibits the same elastic properties in all directions at a given point is called isotropic.
Topic: Material Science
Number of atoms per unit cell of a face centered cubic (FCC) lattice is
Answer: C. 4
Explanation: Number of atoms per unit cell for crystal systems: SC is 1, BCC is 2, and FCC is 4.
Topic: Material Science
The impact strength of a material is an index of its
Answer: D. toughness
Explanation: The impact strength is the resistance of a material to fracture under a sudden impact or shock load, it is a measure of the toughness of the material.
Topic: Material Science
Which of the following order of crystal structure will match with metals Iron - Nickel - Titanium in that order at room temperature?
Answer: D. BCC-FCC-HCP
Explanation: Iron is BCC, Nickel is FCC, and Titanium is HCP at room temperature.
Topic: Manufacturing
In a machining operation cutting speed is reduced by 50%. Assuming n = 0.5, C = 300 in Taylor's equation, the increase in tool life is
Answer: B. 4
Explanation: Taylor's equation is VT^n = C. V1(T1)^0.5 = V2(T2)^0.5 => V(T1)^0.5 = (V/2)(T2)^0.5 => (T2/T1)^0.5 = 2 => T2 = 4*T1. The tool life increases by a factor of 4.
Topic: Manufacturing
In a linear arc welding process, the heat input per unit length is inversely proportional to
Answer: B. welding speed
Explanation: In a linear arc welding process, the heat input per unit length is inversely proportional to welding speed. As we increase welding speed, heat input per unit length decreases due to less time available for heat transfer.
Topic: Manufacturing
The welding process which uses a blanket of fusible granular flux is
Answer: A. submerged arc welding
Explanation: In submerged arc welding, a blanket of fusible granular flux is used to shield the weld zone.
Topic: Manufacturing
In a metal sheet of 3 mm thickness, a hole of 7mm diameter needs to be punched. The yield strength in tension of the sheet material is 120 MPa and its ultimate shear strength is 100 MPa. The force required to punch the hole is
Answer: C. 6.6 kN
Explanation: Punching force F = pi * D * t * tau_s = 3.14 * 7 * 3 * 100 = 6594 N = 6.594 kN (approximately 6.6 kN).
Topic: Metrology
Profile of a gear tooth can be checked by
Answer: D. optical projector
Explanation: Profile of a gear tooth can be checked by an optical projector.
Topic: Metrology
The reflector combined with auto collimator can be used for checking
Answer: D. alignment
Explanation: Auto-Collimator is an instrument used to measure small angular inclinations. It is also used to check straightness, flatness and alignment.
Topic: Industrial Engineering
PERT has following time estimate
Answer: C. three time estimate
Explanation: PERT uses three time estimates: Optimistic time estimate, Pessimistic time estimate, and Most likely time estimate.
Topic: Material Science
Which of the following is an amorphous material
Answer: D. glass
Explanation: Amorphous solids are non-crystalline solids in which the atoms and molecules are not organized in a definite lattice pattern. Such solids include glass, gel, etc.
Topic: Engineering Mathematics
In a party, each person shake hands with every other person present. The total number of handshakes was 45. The number of people in the party is
Answer: B. 10
Explanation: Total number of handshakes for n people is nC2 = n(n-1)/2. So, n(n-1)/2 = 45 => n² - n - 90 = 0. Solving gives n = 10.
Topic: Engineering Mathematics
Two non-zero vectors are parallel if their vector product is
Answer: B. 0
Explanation: Vector product is |a||b|sin(theta). Two non-zero vectors are parallel if the angle between them is zero degrees, making sin(0) = 0, thus their vector product is zero.
Topic: Engineering Mathematics
If Eigen value a matrix A is lambda, then the Eigen value of A² is
Answer: D. lambda²
Explanation: If the Eigen value of a matrix A is lambda, then the Eigen value of A² is lambda².
Topic: Engineering Mathematics
The value of lim(x->infinity) (sin x) / x is equal to
Answer: D. zero
Explanation: The value of lim(x->infinity) (sin x) / x = 0 since sin(x) is bounded between -1 and 1, and dividing by infinity yields zero.
Topic: Engineering Mathematics
If f(x) = (1-x)/(1+x) then f(1/x) is equal to
Explanation: Replacing x with 1/x: f(1/x) = (1 - 1/x)/(1 + 1/x) = (x - 1)/(x + 1) = -((1 - x)/(1 + x)) = -f(x).
Topic: Engineering Mathematics
Inverse Laplace transform of [question incomplete in source,cite: 2]
Explanation: This question was deleted or marked with no answer provided by ISRO due to an incomplete question statement.
Topic: Engineering Mathematics
One dimensional wave equation is
Answer: A. d^2y/dt² = a²(d^2y/dx²)
Explanation: The wave equation is d^2y/dt² = a²(d^2y/dx²). Option (b) is the heat equation, and (c) is the Laplace equation.
Topic: Engineering Mathematics
Which of the following method is said to be a direct method in numerical methods?
Answer: D. Gauss elimination method
Explanation: Gauss elimination method is a direct method for solving a linear system of equations whereas the other options are iterative methods.
Topic: Engineering Mathematics
If X is a normal variable with mean mu and standard deviation sigma, then the mean and standard deviation of the variable Z = (X - mu)/sigma is
Answer: C. 0 and 1 respectively
Explanation: For a standard normal variable Z = (X - mu)/sigma, the mean is 0 and the standard deviation is 1.
Topic: Engineering Mathematics
Example for an elliptic partial differential equation is
Answer: A. U_xx + U_yy = 0
Explanation: U_xx + U_yy = 0 represents the Laplace equation, which is a classic example of a second order linear elliptic partial differential equation.
Topic: Engineering Mathematics
The solution of the equation y'' + y = 0 satisfy the condition y(0) = 1, y(pi/2) = 2, is
Answer: A. cos x + 2 sin x
Explanation: The general solution is y = C1*sin(x) + C2*cos(x). Using y(0) = 1 gives C2 = 1. Using y(pi/2) = 2 gives C1 = 2. Therefore, the equation becomes y = 2*sin(x) + cos(x).
Topic: Strength of Materials
A composite bar made of aluminum and steel is fixed rigidly at supports P and Q as shown in figure. When the temperature of the bar is increased by 10 °C the reactions at the supports are (given E_al = 70 GPa, E_s = 210 GPa, alpha_al = 11E-6 mm/mm °C and alpha_s = 12E-6 mm/mm °C)
Answer: A. 4060 N
Explanation: Total deflection due to temperature rise is (alpha * t * L)_s + (alpha * t * L)_Al = 0.58 mm. Equating this to mechanical elongation (PL/AE)_s + (PL/AE)_Al gives 0.58 = P/7000, which yields P = 4060 N.
Topic: Strength of Materials
Torque, T is applied at the free end of a stepped rod of circular cross section as shown in figure. If the shear modulus of the material is G, the angular twist, at free end will be
Answer: C. 36TL / (G*pi*d^4)
Explanation: When shafts are connected in series, total twist is theta_1 + theta_2. Theta = (TL/GJ)_1 + (TL/GJ)_2. Calculating polar moments of inertia for diamters d and 2d gives a total angular twist of 36TL / (G*pi*d^4).
Topic: Strength of Materials
In most brittle materials, the ultimate strength in compression is larger than the ultimate strength in tension due to
Answer: B. Presence of flaws and microscopic cracks or cavities
Explanation: In brittle materials, the ultimate strength in compression is larger than the ultimate strength in tension due to the presence of flaws and microscopic cracks or cavities that propagate rapidly under tension.
Topic: Theory of Machines
For the spring system given in figure, the equivalent stiffness is
Answer: C. K
Explanation: Upper two springs are in parallel, so equivalent stiffness K1 = K + K = 2K. This equivalent spring is in series with the bottom 2K spring. 1/K_eq = 1/2K + 1/2K = 2/2K = 1/K. Thus, K_eq = K.
Topic: Strength of Materials
A round uniformly tapered bar of length L and Young's modulus E has diameter of 'd' at one end and '2d' at the other end. If the bar is pulled by an axial force F, the extension produced will be
Answer: A. 2FL / (pi*E*d²)
Explanation: Extension produced in a tapered bar is given by delta = 4FL / (pi * d1 * d2 * E). Substituting d1 = d and d2 = 2d yields delta = 4FL / (pi * d * 2d * E) = 2FL / (pi * E * d²).
Topic: Engineering Mechanics
Two blocks A and B of 1 kg each are kept on a flat surface, one above other. The coefficient of friction between each contacting pair is 0.2. If the lower block is pulled with a horizontal force F, the minimum value of F for which the slip occurs between the blocks is nearly
Answer: A. 5.9 N
Explanation: Friction occurs at both the top interface and the ground interface. Normal force at top R_A = 1g. Normal force at bottom R_B = (1+1)g. F = mu*R_A + mu*R_B = 0.2*(3*1*9.81) = 5.886 N, which is approx 5.9 N.
Topic: Theory of Machines
If the natural frequency of a spring mass system on earth is f, its natural frequency on moon where acceleration due to gravity is one-sixth of that on earth will be
Answer: D. f
Explanation: Natural frequency f = (1 / 2*pi) * $\sqrt{k/m}$. It does not depend on gravity, so it remains the same on Earth and the moon.
Topic: Strength of Materials
A solid shaft can resist a bending moment of 6 kN m and a torque of 8 kN m applied together. The maximum torque that the shaft can resist when applied alone is
Answer: C. 10 kN m
Explanation: Equivalent torque T_eq = $\sqrt{M² + T²}$ = $\sqrt{6^2 + 8^2}$ = $\sqrt{36 + 64}$ = 10 kN m.
Topic: Strength of Materials
Two shafts of the same length and material are connected in series, if the ratio of their diameters is 2, then the ratio of their angles of twist will be
Answer: C. 16
Explanation: Angle of twist theta = (T * L) / (G * J). Since J is proportional to d^4, theta is inversely proportional to d^4. Thus, theta_1 / theta_2 = (d_2 / d_1)^4 = (2d/d)^4 = 16.
Topic: Strength of Materials
A concentrated load of F acts on a simply supported beam of span L at a distance of L/3 from left support, the bending moment at this location C is
Answer: C. 2FL/9
Explanation: Taking moment about A: R_B * L = F * (L/3), so R_B = F/3 and R_A = 2F/3. The maximum bending moment at C is M_C = R_A * (L/3) = (2F/3) * (L/3) = 2FL/9.
Topic: Strength of Materials
A solid metal bar of uniform diameter D and length L is hung vertically. If rho is density and E is the Young's Modulus, then the total elongation due to self weight is
Answer: B. rho*L²*g/2E
Explanation: The elongation due to self-weight for a uniform bar hung vertically is delta = (rho * g * L²) / (2E).
Topic: Theory of Machines
A circular solid disc of uniform thickness 20mm, radius 400 mm and mass 10 kg, is used as a flywheel. If it rotates at 300 rpm, the kinetic energy of the flywheel, in Joules is
Answer: A. 395
Explanation: KE = (1/2)*I*omega². I = (m*r²)/2 = (10 * 0.4^2) / 2 = 0.8 kg-m². omega = 2*pi*300/60 = 10*pi rad/s. KE = 0.5 * 0.8 * (10*pi)^2 = 40 * pi² = 394.78 J, approximately 395 J.
Topic: Theory of Machines
If the length of the cantilever beam is reduced to 1/4th, the natural frequency of the mass M at the end of this cantilever beam of negligible mass will be increased by a factor of
Answer: D. 8
Explanation: Deflection delta = (Mg*L³)/(3EI). Natural frequency f is proportional to 1/$\sqrt{delta}$, which means f is proportional to 1/L^(3/2). f2/f1 = (L1/L2)^(3/2) = (L / (L/4))^(3/2) = 4^(3/2) = 8.
Topic: Strength of Materials
The relationship between the linear elastic properties Young's Modulus (E), rigidity modulus (G) and Bulk modulus (K) is given by
Answer: D. 9/E = 1/K + 3/G
Explanation: We know E = (9KG) / (3K + G). Inverting gives 9/E = (3K + G) / KG = 3/G + 1/K.
Topic: Strength of Materials
Euler's critical buckling load for a column fixed at both ends is
Answer: C. 4*pi²*EI / L²
Explanation: When both ends are fixed, the effective length Le = L/2. Euler's load Pe = pi²*EI / Le² = 4*pi²*EI / L².
Topic: Engineering Mechanics
A truck hauls a trailer at 60 km/hour when exerting a steady pull of 600N. If the work is done for 40 minutes, the power required is
Answer: D. 10 kW
Explanation: Velocity V = 60 * (5/18) = 50/3 m/s. Power P = F * V = 600 * (50/3) = 10000 W = 10 kW.
Topic: Theory of Machines
A perfectly balanced rotor shaft supported between short bearings at both ends shows a deflection of 2 mm at middle. Then the critical speed of the shaft in rpm will be nearly,
Answer: B. 670
Explanation: Omega = $\sqrt{g / delta}$ = $\sqrt{9.81 / 0.002}$ = 70.035 rad/s. Critical speed N_c = (60 * Omega) / (2 * pi) = (60 * 70.035) / (2 * 3.14) = 669.12 rpm, which is approximately 670 rpm.
Topic: Machine Design
If an element is loaded as shown in figure below, the Von Mises stress will be close to (Principal stresses: 300 MPa, 150 MPa, -100 MPa)
Answer: B. 350 MPa
Explanation: Using Von Mises theory: (sigma1 - sigma2)^2 + (sigma2 - sigma3)^2 + (sigma3 - sigma1)^2 = 2 * sigma_y^2. Substituting the values gives (-100 - 300)^2 + (300 - 150)^2 + (150 - (-100))^2 = 160000 + 22500 + 62500 = 245000 = 2*sigma_y^2. Thus sigma_y^2 = 122500, making sigma_y = 350 MPa.