Question

A uniform ball of mass ${}^{\prime }{m}^{\prime }$ rolls without sliding on a fixed horizontal surface. The velocity of the lowest point of the ball with respect to the centre of the ball is $V$. Find out the total kinetic energy of the ball.

Answer 1

Linear Kinetic energy $=\frac{1}{2}m{v}^2$

Rotational K.E $=\frac{1}{2}I{\omega }^2$

$I=\frac{2}{5}m{R}^2$ (If ball is solid sphere)

$\therefore K.E_{rot}=\frac{1}{2}\times \frac{2}{5}m{R}^2{\omega }^2=\frac{1}{5}m{v}^2(\because$ pure rolling $\Rightarrow r\omega =v)$

$\therefore$ Total K.E$=\frac{1}{2}m{v}^2+\frac{1}{5}m{v}^2=\frac{7}{10}m{v}^2$