Question

A thin hollow sphere of mass $m$ is completely filled with non-viscous liquid of mass $m$. When the sphere rolls on horizontal ground such that centre moves with velocity $v$, kinetic energy of the system is equal to :

• A. $m{v}^2$
• B. $\frac{4}{3}m{v}^2$
• C. $\frac{4}{5}m{v}^2$
• D. None of these

Answer 1

The correct option is B $\frac{4}{3}m{v}^2$

Non-viscous liquid has only translational kinetic energy.
$\therefore {\text{KE}}_{\text{system}}=$ (Translational + Rotational) K.E of hollow sphere + Translational K.E of liquid
$=\frac{1}{2}m{v}^2+\frac{1}{2}\times I{\left(\omega \right)}^2+\frac{1}{2}m{v}^2$
For pure rolling $v=\omega R$
$\therefore {\text{KE}}_{\text{system}}=\frac{1}{2}m{v}^2+\frac{1}{2}\times \frac{2}{3}m{R}^2{\left(\frac{v}{R}\right)}^2+\frac{1}{2}m{v}^2=\frac{4}{3}m{v}^2$