Question

A solid sphere is placed on a smooth horizontal plane. A horizontal impulse $I$ is applied at a distance $h$ above the central line as shown in the figure. Soon after giving an impulse, the sphere starts rolling. The ratio $h/R$ would be:

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

Answer 1

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

After applying horizontal impulse $J$ horizontal velocity of sphere becomes $v$ as initial linear momentum was $0$

$J=Mv$

Angular impulse about C.M

$=hMv=Iw$

$hMv=\frac{2}{5}M{R}^{2}w$

$w=\frac{5vh}{2R^2}$

While rolling $w=\frac{5vh}{2R^2}$

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