Question

A disc of mass m and radius R is resting on horizontal surface with coefficient of friction $\mu$. If sudden velocity $V_0$ (without any angular velocity) is imparted to disc then time after which disc starts pure rolling is

• A. $\frac{V_0}{\mu g}$
• B. $\frac{2V_0}{\mu g}$
• C. $\frac{2V_0}{3\mu g}$
• D. $\frac{V_0}{3\mu g}$

Answer 1

The correct option is D $\frac{V_0}{3\mu g}$

By conservation of angular momentum about any point of surface:

$m{V}_{0}R=\frac{3}{2}m{R}^2\omega \Rightarrow R\omega =v=\frac{2V_0}{3}$



By, $v=u+at$

$\frac{2V_0}{3}=V_0-\mu gt$

$t=\frac{V_0}{3\mu g}$