Question

A solid sphere of mass $2\text{kg}$ and radius $1\text{m}$ is performing combined rotational and translational motion as shown in figure. Find the total kinetic energy of the solid sphere.

• A. $14\text{J}$
• B. $4\text{J}$
• C. $10\text{J}$
• D. $20\text{J}$

Answer 1

The correct option is A $14\text{J}$

In combined rotational and translational motion,
${\text{K.E}}_{\text{total}}={\text{K.E}}_{\text{translation}}+{\text{K.E}}_{\text{rotation}}$
$\Rightarrow {\text{K.E}}_{\text{total}}=\frac{1}{2}M{v}_0^2+\frac{1}{2}I{\omega }^2...\left(i\right)$
$\text{MOI}$ for solid sphere, $I=\frac{2}{5}M{R}^2$
Putting in Eq $\left(i\right)$, we get
${\text{K.E}}_{\text{total}}=(\frac{1}{2}\times 2\times 2^2)+[\frac{1}{2}\times (\frac{2}{5}\times 2\times 1^2)\times 5^2]$
$\therefore {\text{K.E}}_{\text{total}}=4+10=14\text{J}$