Question

For a body in pure rolling, its rotational kinetic energy is $\frac{1}{2}$ times of its translational kinetic energy. The body should be?

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

Answer 1

The correct option is A

Solid cylinder

Step 1: Given data

Here the body's rotational kinetic energy is $\frac{1}{2}$ times of its translational kinetic energy

Rotational $KE$ $=$ $\frac{1}{2}$ Translational $KE$

Angular velocity $=\omega$

Radius $=R$

Speed $=v$

Rotational inertia $=I$

Step 2: To find which type of body

We know rotational kinetic energy $=\frac{1}{2}$translational kinetic energy

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

The body is in pure rolling, Therefore

$v=R\omega$

$$\begin{gathered} \frac{1}{2}I{\omega }^2=\frac{1}{4}m{R}^2{\omega }^2 \\ I=\frac{1}{2}m{R}^2 \end{gathered}$$

Since this is the Moment of inertia of a solid cylinder, therefore, the body is a Solid cylinder

Therefore the correct answer is Option A