Question

A body rolls down an inclined plane. If its kinetic energy of rotation is $40\%$ of its kinetic energy of translation motion, then the body is

• A. hollow cylinder
• B. ring
• C. solid disc
• D. solid sphere
• E. hollow sphere

Answer 1

Answer: (D)

The ratio of kinetic energies
$\frac{K{E}_{rot}}{K{E}_{\text{trans }}}=\frac{\frac{1}{2}m{v}^2\left(\frac{K^2}{R^2}\right)}{\frac{1}{2}m{v}^2}=\frac{K^2}{R^2}=0.4=\frac{2}{5}$
$\Rightarrow K^2=\frac{2}{5}{R}^2$
$\Rightarrow m{K}^2=\frac{2}{5}m{R}^2$
$\Rightarrow$ Body is a solid sphere