A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be

Options

A. 0,1
B. 1,1
C. 1, 0.5
D. 0,2

Answer

A

Explanation

Here , `m_1 = m, m_2 = 2m`
`u_1 = 2 m//s , u_2 = 0`
Coefficient of restitution , e = 0.5
Let `v_1 and v_2` be their respective velocities after collision.
Applying the law of conservation of linear momentum, we get
`m_1u_1 + m_2u_2 = m_1 v_1 + m_2v_2`
`:. m xx 2 = 2m xx 0 = m xx v_1 + 2m xx v_2`
Or `2m = mv_1 + 2mv_2 " or " 2 = (v_1 + 2v_2) " " .....(i)`
By definition of coefficient of restitution, `e = (v_2 - v_1)/(u_1 - u_2)`
or `e (u_1 - u_2) = v_2 - v_1`
`0.5 (2 - 0) = v_2 - v_1 " or " 1 = v_2 - v_1 " " ......(ii)`
Solving equations (i) and (ii), we get
`v_1 = 0 m//s , v_2 = 1 m//s`.