Question 122: Centre of Mass and Rotational Motion

Question

A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is :

Accepted Answer

$$\begin{aligned}
& \frac{	ext { Linear KE }}{	ext { Rotational K.E }}=\frac{\frac{1}{2} \mathrm{mv}_{\mathrm{cm}}^2}{\frac{1}{2} \mathrm{I} \omega^2} \
& \frac{\mathrm{mv}_{\mathrm{cm}}^2}{\frac{2}{5} \mathrm{mR}^2 \omega^2}=\frac{5}{2} \quad(\mathrm{~V}=\omega \mathrm{R})
\end{aligned}$$

Answer

$\frac{3}{4}$

Answer

$\frac{4}{3}$

Answer

$\frac{5}{2}$

Answer

$\frac{2}{5}$

Centre of Mass and Rotational Motion

A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is :

Choose the correct answer: