First slide

Motion of centre of mass

Question

Two bodies of masses 1 kg and 2 kg are moving in two perpendicular direction with velocities 1 m/s and 2 m/s as shown in figure. The velocity
of the centre of mass (in magnitude) of the system will be:

Moderate

A

3 m/s
B

1.67 m/s
C

1.5 m/s
D

1.37 m/s

Solution

${\vec{v}}_{cm} = \frac{1 \times \hat{i} + 2 \times \hat{j}}{1 + 2} = \frac{\hat{i} + 4 \hat{j}}{3}$
$| \vec{v_{cm}} | = \frac{1}{3} \sqrt{1^{2} + 4^{2}} = \frac{\sqrt{17}}{3} = 1.37 m / s$

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