NTA Abhyas JEE Main2020PhysicsCenter of Mass, Momentum and CollisionPractice
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
Options
- A2 uM m
- B2 um M
- C2 u 1 + m M
- D2 u 1 + M m
Correct answer
C. 2 u 1 + m M
Step-by-step solution
By law of conservation of momentum, Mu = MV + mv …(i) e = | v 1 − v 2 | | u 1 − u 2 | = v - V u ⇒ e = 1 = v - V u ⇒ u = v - V ⇒ Mu = Mv − MV ....(ii) From (i) and (ii), 2 Mu = ( M + m ) v ⇒ v = 2 uM M + m ⇒ v = 2 u 1 + m M