JEE Mains · Physics · STD 11- 8. mechanical properties of solids
A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of \(10^5 \mathrm{~N}\) at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement \(\theta\) of the rod axis from its original position would be : (shear moduli, \(\left.\mathrm{G}=10^{10} \mathrm{~N} / \mathrm{m}^2\right)\)
- A \(1 / 160 \pi\)
- B \(1 / 4 \pi\)
- C \(1 / 40 \pi\)
- D \(1 / 2 \pi\)
Answer & Solution
Correct Answer
(A) \(1 / 160 \pi\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Shear moduli }=\frac{\sigma_{\text {shear }}}{\theta} \\ & 10^{10}=\frac{10^5}{\pi \times 16 \times 10^{-4}} \times \frac{1}{\theta} \\ & \theta=\frac{1}{160 \pi} \text { Radian }\end{aligned}\)
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