Question

A rod $AB$ rests with the end $A$ on rough horizontal ground and the end $B$ against a smooth vertical wall. The rod is uniform and of weight $W$. If the rod is in equilibrium in the position shown in figure. Find normal reaction at $B$.

• A. $W\frac{\sqrt{3}}{2}$
• B. $W\frac{\sqrt{3}}{4}$
• C. $W\frac{2}{\sqrt{3}}$
• D. $W\sqrt{3}$

Answer 1

The correct option is A $W\frac{\sqrt{3}}{2}$

The wall is frictionless so frictional force at $B$ will be zero.

W is weight of the road and acting along $AB$ at $AB/2$ from $A$.

To calculate reaction at $B$, put moment about $A=0$.

$N_{B}sin{30}^0\left(AB\right)-W\left(\frac{AB}{2}\right)cos{30}^0=0$

$⟹N_B=W\frac{\sqrt{(}3)}{2}$