At `t = 0`, the positions and velocities of two particles are as shown in the figure. They are kept on a smooth surface and being mutually attracted by gravitational force. Find the position of centre of mass at `t = 2s`.
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Options

A. X = 5 m
B. X = 7 m
C. X = 3 m
D. X = 2 m

Answer

B

Explanation

(b) As no external force are acting on the system. The velocity of centre of mass will be constant.
`v_(cm) = (1 xx 5 - 1 xx 3)/(1 + 1) = 1 m//s`
Displacement of centre of mass `Delta x_(cm) = 1 xx 2 = 2 m`
Hence position of centre of mass `Delta x_(cm) = 5 + 2 = 7 m`.