Two particles are kept on a smooth surface and they move towards each other. If the position and velocities of the particles at $t = 0$ is as shown in the figure. Then position of the center of mass at $t = 2 s e c$ is

x = 7 m

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x = 5 m

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x = 3 m

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x = 2 m

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Solution

The correct option is A $x = 7 m$
Initial position of centre of mass:
$x_{C M} = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$

$x_{C M} = \frac{1 \times 0 + 1 \times 10}{2} = 5 m$

Velocity of centre of mass
$v_{C M} = \frac{m_{1} v_{1} + m_{2} v_{2}}{m_{1} + m_{2}}$

$v_{C M} = \frac{1 \times 5 - 1 \times 3}{2} = 1 m / s$

Displacement of $C M$ in $2 s e c = v_{C M} \times t = 2 m$

So location of $C M = 5 + 2 = 7 m$

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Two particles are kept on a smooth surface and they move towards each other. If the position and velocities of the particles at t=0 is as shown in the figure. Then position of the center of mass at t=2 sec is

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