Question

A solid ball of mass m and radius R is given linear velocity V and no angular velocity and placed on a rough surface. what is the velocity of centre of mass when ball starts pure rolling.

Answer 1

Solid ball=sphere]

$\overline{\tau }=\frac{d{i}_{system}}{dt}$

Torque is zero about the points (p) lying on horizontal surface.

So, Angular momentum of system conserve about point (P,Q)

$\begin{array}{c}{L}_i=L_f\\ M{V}_{0}R=MVR+I.w\left(I=\frac{2}{5}M{R}^2\right)\\ M{V}_{0}R=MVR+\frac{2}{5}M{R}^2\frac{V}{R}\\ V=\frac{5V_0}{7}\end{array}$