Question

A solid sphere rests on a horizontal surface, A horizontal impulse is applied at height $h$ from the centre. The sphere starts rotating just after the application of impulse. The ratio $h/R$ will be

• A. $\frac{1}{2}$
• B. $\frac{2}{5}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

The correct option is B $\frac{2}{5}$

Let the force act for time t.

So, $F\times t=I$ .......(1)

Inertia of solid sphere is $I=2M{R}^2/5$ .......(2)

writing torque about center,

$I\alpha =Fh$ .........(3)

As linear motion is given as $F=ma$ ..........(4)

and $v=\omega R$

From $\left(1\right),\left(2\right),\left(3\right)and\left(4\right)$,

$\frac{h}{R}=\frac{2}{5}$