1) 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. The value of v is A) $\frac{2uM}{m}$ B) $\frac{2um}{M}$ C) $\frac{2u}{1+m/M}$ D) $\frac{2u}{1+ M/m}$ Answer: Option CExplanation:By law of conservation of momentum, Mu = MV +mv ...(1) Also e = $\frac{|v_{1}-v_{2}|}{|u_{1}-u_{2}|}\Rightarrow Mu = Mv-MV$ ....(2) From (1) and (2), 2Mu = (M+m)v $\Rightarrow v = \frac{2uM}{M+m}$ v = $\frac{2u}{1+m/M}$
