A system of two particles is having masses m_1 and m_2. If the particle of mass m_1 is pushed towards the centre of mass of particles through a distance d, by what distance the particle of mass m_2 s…

Question

A system of two particles is having masses m_1 and m_2. If the particle of mass m_1 is pushed towards the centre of mass of particles through a distance d, 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?

Accepted Answer

Correct answer: C. (c) Initial position of centre of mass; r_ cm= m_1x_1+m_2x_2m_1+m_2 … . . (i ) Here, x_1 and x_2 are the distances of mass m_1 and m_2 from centre of mass respectively. In second case, r_ cm^ '= m_1(x_1+d)+m_2(x_2+d^ ')m_1+m_1 … . . ( ii ) Here, d and d^ ' are the displacement of mass m_1 and m_2 respectively. According to question, r_ cm=r_ cm^ ' ∴ m_1x_1+m_2x_2m_1+m_2= m_1(x_1+d)+m_2(x_2+d^ ')m_1+m_2 ⇒d^ '= m_1m_2d

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

Solution

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