question_answer

A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After collision their final velocities are V and v respectively. The value of v is                         [MP PET 1995]

A)          \[\frac{2uM}{m}\]        

B)          \[\frac{2um}{M}\]

C)          \[\frac{2u}{1+\frac{m}{M}}\]                          

D)          \[\frac{2u}{1+\frac{M}{m}}\]

Correct Answer: C

Solution :

                 \[{{v}_{2}}=\left( \frac{{{m}_{2}}-{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}} \right)\ {{u}_{2}}+\frac{2{{m}_{1}}{{u}_{1}}}{{{m}_{1}}+{{m}_{2}}}\]\[=\frac{2Mu}{M+m}=\frac{2u}{1+\frac{m}{M}}\]