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

A ball moving with velocity 2 m/s collides head on with another statio

1.	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
Answer» 0,1 1,1 1, 0.5 0,2 Solution :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`.