Question 111 of 280

An object of mass $8kg$ is hanging from one end of a uniform rod $CD$ of mass $2kg$ and length $1m$ 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 $g=10m{s}^{-2}$)

A$240N$B$90N$C$300N$D$30N$

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Answer: (C) $300N$

Let $T$ be the tension in cable.
Since the system is at equilibrium, the net torque, about an axis perpendicular to the plane and passing through the point of contact of the rod and the wall, is zero. Therefore, torque about point $C$
$T\sin 30^{\circ}\times 60=mg\times 50+8g\times 100$
$\dfrac{T}{2}\times 60=20\times 50+80\times 100$
$\Rightarrow 3T=100+800$
$\Rightarrow 300N$.