A body of mass 2 kg makes an elastic collision (head-on) with another body at rest and continue to move in the original direction at a speed equal to `(1/3)^(rd)` of its original speed. The mass of second body is

Options

A. `2kg`
B. `3 kg`
C. `1 kg`
D. `4 kg`

Answer

C

Explanation

`u_1 = u, u_2 = 0, v_1 = u/3 , v_2 = v`
`e = 1 implies (v - u/3)/(u - 0) = 1 implies v - u/3 = u therefore v = (4u)/3`
From the law of conservation of momentum, `m_1u_1 + 0=m_1v_1 +m_2v_2`
`m_1 u = m_1 u/3 + m_2 (4u)/3 implies m_2 = (m_1)/2 = 2/2 = 1 kg`