Question

A thin hollow sphere of mass $m$ is completely filled with an ideal liquid of mass $m$. When sphere rolls with a velocity $v$, kinetic energy of the system is equal to:

• A. $m{v}^2/2$
• B. $m{v}^2$
• C. $4m{v}^2/3$
• D. $4m{v}^2/5$

Answer 1

The correct option is C $4m{v}^2/3$

The fluid does not undergo rotational motion.

KE(Translational)$=\frac{1}{2}m{v}^2+\frac{1}{2}m{v}^2=m{v}^2$

KE(Rotational)$=\frac{1}{2}I{\omega }^2=\frac{1}{2}\times \frac{2}{3}m{R}^2\cdot \frac{v^2}{R^2}=\frac{1}{3}m{v}^2$

$\therefore$ Total KE$=\frac{1}{3}m{v}^2+m{v}^2=\frac{4}{3}m{v}^2$