Question

A sphere has only translational velocity $V_0=2r\omega$ when placed on rough horizontal surface with frictional coefficient m. If r is radius then the time in which pure rolling starts is

• A. $\frac{2r\omega }{7\mu g}$
• B. $\frac{4r\omega }{7\mu g}$
• C. $\frac{r\omega }{7\mu g}$
• D. $\frac{2\sqrt{2}r\omega }{7\mu g}$

Answer 1

The correct option is B

$\frac{4r\omega }{7\mu g}$

$a=\frac{f}{m}=\mu g\&\alpha =\frac{\tau }{I}=\frac{5\mu g}{2r}$

velocity after time t.

$V=V_0-\mu gt{\omega }^{\prime }=\alpha t=\frac{5\mu g}{2r}t$

Pure rolling start when

$V=r{\omega }^{\prime }sot=\frac{4r\omega }{7\mu g}$