Q 11-06-110JEE MainJEE Main 2023 (25 Jan, Shift 1)Medium
An object of mass $8\ \text{kg}$ is hanging from one end of a uniform rod $CD$ of mass $2\ \text{kg}$ and length $1\ \text{m}$ pivoted at its end $C$ on a vertical wall as shown in figure. It is supported by a cable $AB$ such that the system is in equilibrium. The tension in the cable is (Take $g=10\ \text{m s}^{-2}$)
Answer: (C) $300\ \text{N}$
Take torques about $C$. The cable acts at $B$ ($0.6\ \text{m}$) at $30^\circ$ to the rod; the rod's weight acts at $0.5\ \text{m}$ and the load at $1\ \text{m}$:
$$T\sin30^\circ\times0.6=20\times0.5+80\times1=90$$
$$T=\frac{90}{0.3}=300\ \text{N}$$
Solution by Sreeraj P, M.Sc Physics