A ball moving with velocity 2 ~ms ⁻¹ collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5 , then their velocities (in ms ⁻¹ ) after collision will be

Step-by-step solution

If two bodies collide head on with coefficient of restitution e = v ₂- v ₁ u ₁- u ₂ From the law of conservation of linear momentum array r m ₁ u ₁+ m ₂ u ₂= m ₁ v ₁+ m ₂ v ₂ v ₁= [ m ₁- em ₂ ~m ₁+ m ₂ ] u ₁+ [ (1+ e ) m ₂ ~m ₁+ m ₂ ] u ₂ array Substituting u ₁=2 ~ms ⁻¹, u ₂=0, ~m ₁= m and m ₂=2 ~m , e =0.5 we get array lc we get & v ₁= [ m - m m +2 ~m ] 2 & v ₁=0 array Similarly, aligned v ₂ & = [ (1+ e ) m ₁ ~m ₁+ m ₂ ] u ₁+ [ m ₂- em ₁ ~m ₁+ m ₂ ] u ₂ & = [ 1.5 m 3 ~m ] 2 & =1 ~ms ⁻¹ aligned