First slide

Motion of centre of mass

Question

Three bodies having masses 5 kg, 4 kg and 2 kg are moving at the speeds of $5 {ms}^{- 1}, 4 {ms}^{- 1} and 2 {ms}^{- 1},$
respectively along X-axis. The magnitude of velocity of centre of mass is [AllMS 2018]

Easy

A

$1.0 {ms}^{- 1}$
B

$4 {ms}^{- 1}$
C

$0.9 {ms}^{- 1}$
D

$1.3 {ms}^{- 1}$

Solution

Velocity of centre of mass,
$ν_{CM} = \frac{m_{1} v_{1} + m_{2} v_{2} + m_{3} 3}{m_{1} + m_{2} + m_{3}}$
Given, $m_{1} = 5 kg, v_{1} = 5 {ms}^{- 1},$
$m_{2} = 4 kg, v_{2} = 4 {ms}^{- 1}, m_{3} = 2 kg and v_{3} = 2 {ms}^{- 1}$
Substituting all these values in above equation, we get
$ν_{CM} = \frac{5 \times 5 + 4 \times 4 + 2 \times 2}{5 + 4 + 2} = \frac{25 + 16 + 4}{11}$
$∴ v_{CM} = \frac{45}{11} = 4.09 \approx 4 {ms}^{- 1}$

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