Question

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

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

Answer 1

The correct option is C

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

$\text{K.E}=\left({\text{KE}}_{\text{hollow sphere}}\right)+\left({\text{KE}}_{\text{liquid}}\right)=({\text{KE}}_{\text{h.s.}}{)}_{\text{trans}}+({\text{KE}}_{\text{rot}})+({\text{KE}}_{\text{liquid}}{)}_{trans}$

$=\frac{1}{2}\left(m{v}^2\right)+\frac{1}{2}\left(\frac{2}{3}m{r}^2\right){\left(\frac{v}{r}\right)}^2+\frac{1}{2}m{v}^2=\frac{4}{3}m{v}^2$

Due to the absence of friction, the liquid does not rotate. It only translates.