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. `(2um)/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))`
`v=(2Mu)/(M+m)" "( :' u_(2)=0)`
`v=(2u)/(1+m/M)`