Question

A sphere of mass and radius R rests on sufficiently rough inclined plane in equilibrium as shown in the figure . Find the tension in the string.

Answer 1

Let the tension in string is $T$.

Since the body is in equilibrium, net torque must be zero.

Taking torque about point $O$.

$mg\sin \theta \times R=T\times 2R$
$T=\frac{mg\sin 30°}{2}$

$T=\frac{mg}{4}$