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

B

Explanation

If target is at rest, then final velocity of bodies are

`v_(1) = (m_(1)-m_(2))/(m_(1)+m_(2))u_(1)`...................(i)
and `v_(2) = (2m_(1)u_(1))/(m_(1)+m_(2))`.................(ii)
From eqs (i) and (ii), `v_(1)/v_(2) = (m_(1)-m_(2))/(2m_(1)) = 2/5 rArr (m_(1))/(m_(2)) = 5`