Question

A uniform heavy rod $AB$ of length $L$ and weight $W$ is hinged at $A$ and tied to a weight $W_1$ by a string at $B$, the massless passes over a frictionless pulley (of negligible dimensions) at $C$ as shown in the figure. If the rod is in equilibrium at horizontal configuration, then

• A. $W_1=W$
• B. $W_1=\frac{W}{2}$
• C. $W_1=\sqrt{2}W$
• D. $W_1=\frac{W}{\sqrt{2}}$

Answer 1

The correct option is D $W_1=\frac{W}{\sqrt{2}}$

If $T$ be the tension in the string $BC$ and since it passes over a smooth pulley$C,$

therefore$,$ $T=w_1$

$\begin{array}{c}ReactionofBis\frac{w}{2},\\ \frac{w}{2}=T\cos {45}^0=w_1\times \frac{1}{\sqrt{2}}\\ or,w_1=\frac{w}{\sqrt{2}}\end{array}$

Hence,

option $\left(D\right)$ is correct answer.