A ball of mass moving with a velocity u collides head on with a ball B of mass m at rest. If the coefficient of restitution is e. the ratio of final velocity of B to the initial velocity of A is

Options

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

Answer

C

Explanation

According to the principle of conservation of linear momentum, `"mu"_(1)+0 =m v_(1) +mv_(2)`
`:. u_(1) = v_(1) +v_(2)" "...(1)`
The coefficient of restitution `e= (v_(2)-v_(1))/(u_(1)-u_(2))`
But `:. u_(2) = 0 `
`:.e= (v_(2)-v_(1))/(u_(1)):. eu_(1)=v_(2)-v_(1)" "...(2)`
Adding (1) and (2), we get
`u_(1) (l+e) =2v_(2) :. v_(2) (u_(1)(e+l))/(2)`
`:. ("Final velocity of B")/("Initial velocity of A")=(v_(2))/(u_(1))`
`= (u_(1) (e+1))/(2u_(1))=(e+1)/(2)`