Question

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is $50\%$ of its translational kinetic energy. The body is :

• A. Solid sphere
• B. Solid cylinder
• C. Ring
• D. Hollow cylinder

Answer 1

The correct option is B Solid cylinder

Give:
$(KE{)}_R=50\%\text{of}(KE{)}_T=\frac{1}{2}\times (KE{)}_T$

$\Rightarrow \frac{1}{2}I{\omega }^2=\frac{1}{2}\times \frac{1}{2}m{v}^2$

Here, body moves without slipping, $v=R\omega$

$\therefore I=\frac{1}{2}m{R}^2$

And we know that, $\text{MOI}$ of disc or solid cylinder is $m{R}^2/2$.

Hence, option $\left(\text{B}\right)$ is correct.