Question

A system of two particles is having masses m₁ and m₂. If the particle of mass m₁ is pushed towards the centre of mass of particles through a distance d, 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?

Options

• `m_1/(m_1 + m_2) d` 

• d

• `m_1/m_2 d`

• `m_2/m_1 d`

Answer 1

`m_1/m_2 d`

Explanation:

m₁x₁ = m₂x₂  .....(i)

m₁(x₁ – d) = m₂(x₂ – d')  ......(ii)

∴ m₁x₁ – m₁d = m₂x₂ – m₂d'

m₁d = m₂d'  ......[From (i)]

∴ d' = `m_1/m_2 d`