A sphere P of mass m moving with velocity u collides head on with another sphere Q of mass m which is at rest . The ratio of final velocity of Q to initial velocity of P is
( e = coefficient of restitution )

Options

A. `(e - 1)/(2)`
B. `[(e+ 1)/(2)]^(1//2)`
C. `(e + 1)/(2)`
D. `[(e+1)/(2)]^(2)`

Answer

C

Explanation

Here , `m_(1) = m_(2) = m , u_(1) = u,u_(2) = 0`
Let `v_(1) , v_(2)` be their velocities after collision
According to principle of conservation of linear momentum
mu + 0 = `m(v_(1) + v_(2))`
or `v_(1) + v_(2) = v " " … (i)`
By definition , `e = (v_(2) - v_(1))/(u - 0) `
or `v_(2) - v_(1) = eu " " ... (ii)`
Adding Eqs. (i) and (ii) , we get
`v_(2) = (u (1 + e))/(2) implies (v_(2))/(u) = (1 + e)/(2)`