In the system of two particles of masses ' $\mathrm{m}_1$ ' and ' $\mathrm{m}_2$ ', the first particle is…

In the system of two particles of masses ' $\mathrm{m}_1$ ' and ' $\mathrm{m}_2$ ', the first particle is moved by a distance 'd' towards the centre of mass. To keep the centre of mass unchanged, the second particle will have to be moved by a distance
  1. $\frac{\mathrm{m}_2}{\mathrm{~m}_1} \mathrm{~d}$, towards the centre of mass.
  2. $\frac{m_1}{m_2} d$, away from the centre of mass.
  3. $\frac{\mathrm{m}_1}{\mathrm{~m}_2} \mathrm{~d}$, towards the centre of mass.
  4. $\frac{m_2}{m_1} \mathrm{~d}$, away from the centre of mass.

Solution


$\begin{array}{ll} & m_1 x_1=m_2 x_2 ...(i)\\ & m_1\left(x_1-d\right)=m_2\left(x_2-d^{\prime}\right) ...(ii)\\ \therefore \quad & m_1 x_1-m_1 d=m_2 x_2-m_2 d^{\prime} \\ & m_1 d=m_2 d^{\prime} \\ \therefore \quad & d^{\prime}=\frac{m_1}{m_2} d \end{array}$ ...[From (i)] .

Asked in: MHT CET 2024 (09 May Shift 1)

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