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

Step-by-step solution

Let mass of first ball be m i.e. m₁=m Mass of second ball m ₂=2 ~m Velocity of first ball before collision u ₁=2 ~m / s Velocity of second ball before collision u ₂= om / s Given : e =0.5 So, velocity of first ball after collision v ₁= ( m ₁- em ₂ ) u ₁+(1+ e ) m ₂ u ₂ ~m ₁+ m ₂ v ₁= [ m -0.5(2 ~m )](2)+(1+0.5)(2 ~m )(0) m +2 ~m = om / s Velocity of second ball after collision v ₂= ( m ₂- em ₁ ) u ₂+(1+ e ) m ₁ u ₁ ~m ₁+ m ₂ v ₂= [2 ~m -0.5 ~m ](0)+(1+0.5)( m )(2) m +2 ~m =1 ~m / s Correct answer is option A.