Question

A solid sphere of radius $R$ rests on a horizontal surface. A horizontal impulse is applied on sphere at height $h$ from centre, as shown in figure below. The sphere starts rolling just after the application of impulse. What will be the ratio $\frac{h}{R}$ ?

• A. $\frac{1}{2}$
• B. $\frac{2}{5}$
• C. $\frac{1}{5}$
• D. $\frac{2}{3}$

Answer 1

Answer: (B)

Rolling is rotation about point of contact. Applying impulse momentum equation about P.
$J\left(R + h\right)=Ι_{P}\times \omega $ (i)
and $J=mv$ (ii)
As sphere rolls $v=\omega R$ , and $Ι=\frac{2}{5}mR^{2}+mR^{2}=\frac{7}{5}mR^{2}$
After solving, we get $\frac{h}{R}=\frac{2}{5}$