JEE Main · 2006 · 30 Apr 2006 · Offline · Conservation of Momentum

Consider a two particle system with particles having masses

m_{1}

and

m_{2}

. If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

(A)d
(B) $\frac{m _{2}}{m _{1}} d$
(C) $\frac{m _{1}}{m _{1} + m _{2}} d$
(D) $\frac{m _{1}}{m _{2}} d$ ✓ Correct

Answer: (D)

Solution

The centre of mass stays put only if the mass-weighted displacements about it cancel, i.e.

m_{1} d = m_{2} x

in magnitude, with the two particles moving in opposite senses. Solving for the shift of the second particle gives

x = \frac{m _{1}}{m _{2}} d

. So the second particle must be moved outward through

\frac{m _{1}}{m _{2}} d

JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option

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