Q 11-08-110JEE MainJEE Main 2025 (4 Apr, Shift 2)Medium
A cylindrical rod of length $1\ \text{m}$ and radius $4\ \text{cm}$ is mounted vertically. It is subjected to a shear force of $10^5\ \text{N}$ at the top. Considering an infinitesimally small displacement of the upper edge, the angular displacement $\theta$ of the rod axis from its original position would be: (shear modulus $G = 10^{10}\ \text{N/m}^2$)
Answer: (A) $\dfrac{1}{160\pi}$
The shear force acts over the top face, area $\pi r^2 = \pi\times(0.04)^2 = 16\pi\times10^{-4}\ \text{m}^2$.
$$\theta = \frac{\text{shear stress}}{G} = \frac{F}{\pi r^2G} = \frac{10^5}{16\pi\times10^{-4}\times10^{10}} = \frac{1}{160\pi}\ \text{rad}$$
Solution by Sreeraj P, M.Sc Physics