First slide

Motion of centre of mass

Question

A body of mass m₁ = 4 kg moves at $5 \hat{i} {ms}^{- 1}$ and another body of mass m₂ = 2 kg moves at $10 \hat{i} {ms}^{- 1}$ . The kinetic energy of centre of mass is

Moderate

A

$\frac{200}{3} J$
B

$\frac{500}{3} J$
C

$\frac{400}{3} J$
D

$\frac{800}{3} J$

Solution

Velocity of centre of mass,
   $v_{CM} = \frac{m_{1} \frac{{dr}_{1}}{dt} + m_{2} \frac{{dr}_{2}}{dt}}{m_{1} + m_{2}} = \frac{4 \times 5 \hat{i} + 2 \times 10 \hat{i}}{4 + 2} = \frac{40 \hat{i}}{6} = \frac{20}{3} \hat{i}$
The kinetic energy of centre of mass,
   $K = \frac{1}{2} {mv}_{CM}^{2} = \frac{1}{2} \times (4 + 2) \times \frac{20 \times 20}{3 \times 3}$
   $= \frac{1}{2} \times 6 \times \frac{20 \times 20}{3 \times 3} = \frac{400}{3} J$

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