A system of two particles is having masses $m_{1}$ and $m_{2}$ . If the particle of mass $m_{1}$ is pushed towards the center of mass of particles through a distance, $d$ , then determine by what distance the particle of mass $m_{2}$ should be moved so as to keep the centre of mass of particles at the original position?

\frac{m_{1}}{m_{2} + m_{2}} d

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d

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\frac{m_{1}}{m_{2}} d

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\frac{m_{2}}{m_{1}} d

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Solution

The correct option is C $\frac{m_{1}}{m_{2}} d$
Position of center of mass $x_{c m} = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$

Shift in position of center of mass $Δ x_{c m} = \frac{m_{1} Δ x_{1} + m_{2} Δ x_{2}}{m_{1} + m_{2}}$

Given : $Δ x_{c m} = 0$ $Δ x_{1} = d$

$∴$ $0 = \frac{m_{1} d + m_{2} Δ x_{2}}{m_{1} + m_{2}}$

$⟹ Δ x_{2} = - \frac{m_{1}}{m_{2}} d$

Thus $m_{2}$ must also be shifted towards the center of mass by a distance $\frac{m_{1}}{m_{2}} d$ .

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A system of two particles is having masses m1 and m2. If the particle of mass m1 is pushed towards the center of mass of particles through a distance, d, then determine by what distance the particle of mass m2 should be moved so as to keep the centre of mass of particles at the original position?

The correct option is C m1m2dPosition of center of mass xcm=m1x1+m2x2m1+m2Shift in position of center of mass Δxcm=m1Δx1+m2Δx2m1+m2Given : Δxcm=0 Δx1=d∴ 0=m1d+m2Δx2m1+m2⟹ Δx2=−m1m2dThus m2 must also be shifted towards the center of mass by a distance m1m2d.