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

Options

A. `(2uM)/(m)`
B. `(2muM)/(M)`
C. `(2u)/(1+(m)/(M))`
D. `(2u)/(1+(M)/(m))`

Answer

C

Explanation

`v_(2)= ((m_(2)-m_(1))/(m_(1) + m_(2))) u_(2) + (2m_(1)u_(1))/(m_(1) + m_(2))= (2M u)/(M+m)= (2u)/(1+ (m)/(M))`