A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of 10^5 ~N at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement θ

Correct answer: A. 1 / 160 π aligned & Shear moduli = σ_ shear θ & 10^ 10 = 10^5 π × 16 × 10^ -4 × (1)/(θ) & θ=(1)/(160 π) Radian aligned

JEE Main 20254 AprilEvening Shift

JEE Main 2025 · 4 April · Evening Shift · Physics · Mechanical Properties of Solids

A cylindrical rod of length 1 m and radius 4 cm is mounted...

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. $1 / 160 \pi$

\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}