First slide

Rolling motion

Question

A thin metal disc of radius 0.25 m and mass 2 kg starts from rest and rolls down an inclined plane. If its rotational kinetic energy is 4 J at the foot of the inclined plane, then its linear velocity at the same point is

Moderate

A

$1.2 {ms}^{- 1}$
B

$2 \sqrt{2} {ms}^{- 1}$
C

$20 {ms}^{- 1}$
D

$2 {ms}^{- 1}$

Solution

Here, r = 0.25 m and m = 2 kg
Rotational KE $= \frac{1}{2} {Iω}^{2} = \frac{1}{2} \times (\frac{1}{2} {mr}^{2}) ω^{2}$
$\begin{array}{l} \Rightarrow 4 = \frac{1}{4} {mv}^{2} = \frac{1}{4} \times 2 v^{2} \\ ∴ v = \sqrt{8} = 2 \sqrt{2} {ms}^{- 1} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App