A body P of mass m moving with kinetic energy k and momentum p undergoes a one-dimensional elastic collision with a body of mass 2 m at rest. After the collision, the ratio of the kinetic energy of P to that of Q is

Options

A. `1/8`
B. `1/4`
C. `1/9`
D. `8/9`

Answer

A

Explanation

`v_1 = ((m_1 + m_2)/(m_1 + m_2))u_1 + (2m_1u_2)/(m_1 + m_2)`
`v_2 = (2m_1u_1)/(m_1 + m_2) + ((m_2 - m_1)/(m_1 + m_2))u_2`
Here `u_2 = 0, m_1 = m and m_2 = 2m`
`v_1 = -u/3 and v_2 = (2u)/3`
`(k_1)/(k_2) = (1/2 m(u/3)^2)/(1/2 xx 2m xx ((2u)/(3))^2) = ((1/3)^2)/((2/3)^2) = (1/9)/(8/9) = 1/8`