Question

A ring of masses $0.3kg$ and radius $0.1m$ and a solid cylinder of mass $0.4kg$ and of the same radius are given the same kinetic energy and released simultaneously on a flat horizontal surface such that they begin to roll as soon as released towards a wall which is at the sam edistance from the ring and the cylinder. The rolling friction in both the cases is negligible. The cylinder will reach the wall first.

• A. True
• B. False

Answer 1

The correct option is A True

Let $K$ be the kinetic energy given to the ring and cylinder.

we know $K=\frac{1}{2}I{\omega }^2$

so, $\omega =\sqrt{\frac{2K}{I}}⟹\omega \propto \frac{1}{\sqrt{I}}$

let $R$ be the given radius of ring and cylinder.

therefore ,$I_{ring}=0.3R^2>I_{cylinder}=\frac{0.4}{2}{R}^2$

So ${\omega }_{ring}<{\omega }_{cylinder}$

Also $v=\omega r$ .........................(pure rolling)

$v_{cylinder}>v_{ring}⟹t_{cylinder}<t_{ring}$

Hence option A is correct.