A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m…

A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After the collision, their final velocities are V and v respectively. Then v is
  1. 2uMm
  2. 2umM
  3. 2u1+mM
  4. 2u1+Mm

Solution

By law of conservation of momentum,

Mu=MV+mv…(i)
 e=|v1−v2||u1−u2|=v-Vu⇒e=1=v-Vu⇒u=v-V
⇒Mu=Mv−MV ....(ii)
From (i) and (ii), 2Mu=(M+m)v

⇒v=2uMM+m⇒v=2u1+mM

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