A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest. The kinetic energy of the balls after the collision is `3/4` th of the original. Find the coefficient of restitution.

Options

A. `1/(sqrt2)`
B. `1/(sqrt3)`
C. `1/(2sqrt(2))`
D. `1/(sqrt5)`

Answer

A

Explanation

`v_1 ((m_1 - em_2))/(m_1 + m_2) u_1 = ((1 + e)m_2)/(m_1 + m_2) u_2 , v_2 = ((1 + e)m_1)/(m_1 + m_2) u_2 + (m_2 - em_1)/(m_1 + m_2) u_2`
`u_1 = v, u_2 = 0 m_1 = m_2 = m`
`therefore v_1 = ((1- e))/(2) v " " .....(1)`
`v_2 = ((1 + e))/(2) v .....(2)`
`1/2 mv_1^2 + 1/2 mv_2^2 = 3/4 1/2 mv^2 , 1/2 m ((1 - e)^2)/(4) v^2 + 1/2 m ((1 + e)^2)(4) v^2 = 3/4 xx 1/2 mv^2`
`(1 - e)^2 + (1 + e)^2 = 3 , 1 + e^2 + 1 + e^2 = 3 , 2 + 2e^2 = 3`
`2e^2 = 1 , e^2 = 1/2 , e = 1/(sqrt2)`