GATE XE (Engineering Sciences) 2022 - Question 46

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Section: Solid Mechanics | 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

Figure for question 46, GATE XE (Engineering Sciences) 2022

  • A. a twisting moment π‘ƒπ‘…αˆΊ1 ࡆcos πœƒαˆ»π’, a bending moment 𝑃𝑅sin πœƒ 𝐣, and a shear force ࡆ𝑃 𝐀
  • B. a twisting moment π‘ƒπ‘…αˆΊ1 ࡆsin πœƒαˆ»π’, a bending moment 𝑃𝑅cos πœƒ 𝐣, and a shear force 𝑃 𝐀
  • C. a twisting moment π‘ƒπ‘…αˆΊcos πœƒΰ΅†1ሻ𝐒, a bending moment ࡆ𝑃𝑅sin πœƒ 𝐣, and a shear force ࡆ𝑃 𝐀
  • D. a twisting moment 𝑃𝑅sin πœƒπ’, a bending moment π‘ƒπ‘…αˆΊ1 ࡆcosαˆ»πœƒ 𝐣, and a shear force 𝑃 𝐀

Answer: A. a twisting moment π‘ƒπ‘…αˆΊ1 ࡆcos πœƒαˆ»π’, a bending moment 𝑃𝑅sin πœƒ 𝐣, and a shear force ࡆ𝑃 𝐀

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