Question

A horizontal uniform rod of mass ${}^{\prime }{m}^{\prime }$ has its left end hinged to the fixed incline plane, while its right end rests on the top of a uniform cylinder of mass ${}^{\prime }{m}^{\prime }$ which in turn is at rest on the fixed inclined plane as shown. The coefficient of friction between the cylinder and rod, and between the cylinder and inclined plane, is sufficient to keep the cylinder at rest.


The magnitude of normal reaction exerted by the rod on the cylinder is

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

Answer 1

The correct option is C $\frac{mg}{2}$

Let $L$ be the length of rod. As rod is in equilibrium
$\therefore$ Balancing torque about hinge


$N:$ Normal force exerted by cylinder on rod
$\therefore mg\times \frac{L}{2}=N\times L$
$\Rightarrow N=\frac{mg}{2}$

According to Newton's 3rd law,
Magnitude of normal reaction exerted by the rod on the cyclinder is also $\frac{mg}{2}.$