Question

A solid sphere is given velocity V and angular velocity $\omega$ as shown in figure. If $\omega =\frac{V}{2R}$, final velocity of sphere when pure rolling starts is

• A. $\frac{6}{7}$ V
• B. $\frac{7}{6}$ V
• C. $\frac{5}{7}$ V
• D. $\frac{3}{5}$ V

Answer 1

The correct option is A $\frac{6}{7}$ V

By COAM about P.

$L_i=L_f$
$MVR+\frac{2}{5}M{R}^2\omega =M{V}_{0}R+\frac{2}{5}M{R}^2{\omega }_0$

$MVR+\frac{2}{5}M{R}^2\times \frac{V}{2R}=M{V}_{0}R+\frac{2}{5}M{R}^2\times \frac{V_0}{R}$

$\frac{6}{5}MVR=\frac{7}{5}M{V}_{0}R\Rightarrow V_0=\frac{6}{7}V$