First slide

Centre of mass(com)

Question

Two particles are shown in the figure. At t=0, a constant force F=6 N starts acting on the 3 kg man.
Find the velocity of the centre of mass of these particles at t=5 s

Moderate

A

5 m/s
B

4 m/s
C

6 m/s
D

3 m/s

Solution

Method 1: Acceleration of 3 kg:
$a_{2} = \frac{6}{3} = 2 m / s^{2}$
$Velocity of 3 kg at t = 5 s : v_{2} = u_{2} + a_{2} t = 0 + 2 \times 5 = 10 m / s$
$v_{CM (t = 5 s)} = \frac{2 \times 0 + 3 \times 10}{2 + 3} = 6 m / s$
Method 2:
$\begin{array}{l} a_{CM} = \frac{F}{m_{1} + m_{2}} = \frac{6}{2 + 3} = 1.2 m / s^{2} \\ v_{CM} = u_{CM} + a_{CM} t = 0 + 1.2 \times 5 = 6 m / s \end{array}$

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