A thin hollow sphere of mass $m$ is completely filled with a liquid of mass $m$. When the sphere rolls with…
A thin hollow sphere of mass $m$ is completely filled with a liquid of mass $m$. When the sphere rolls with a velocity $v$, kinetic energy of the system is (neglect friction)
$\frac{1}{2} m v^2$
$m v^2$
$\frac{4}{3} m v^2$
$\frac{4}{5} m v^2$
Solution
$\begin{aligned} \text { Total energy } & =\mathrm{KE}+\text { rotational } \mathrm{KE} \\ & =\frac{1}{2}(2 m) v^2+\frac{1}{3} m v^2 \\ & =\frac{4}{3} m v^2\end{aligned}$