Question

A thin hollow sphere of mass $m$ is completely filled with a liquid of mass $m$. When the sphere rolls with a velocity $\upsilon$, kinetic energy of the system is (neglect friction):

• A. $\frac{1}{2}{m\upsilon }^2$
• B. ${m\upsilon }^2$
• C. $\frac{4}{3}{m\upsilon }^2$
• D. $\frac{4}{5}{m\upsilon }^2$

Answer 1

The correct option is C $\frac{4}{3}{m\upsilon }^2$

$K.E_{system}=K.E_{hollowsphere}+K.E_{liquid}$

$=(K.E_{HS}{)}_{trans}+(K.E_{HS}{)}_{rot}+(K.E_{liquid}{)}_{trans}$

$=\frac{1}{2}m{v}^2+\frac{1}{2}\left(\frac{2}{3}m{r}^2\right){\left(\frac{v}{r}\right)}^2+\frac{1}{2}m{v}^2$

$=\frac{4}{3}m{v}^2$