A ball `P` moving with a speed of `v ms^-1` collides directly with another identical ball `Q` moving with a speed `10 ms^-1` in the opposite direction. P comes to rest after the collision. If the coefficient of restitution is 0.6, the value of v is

Options

A. 30 `ms^(-1)`
B. 40 `ms^(-1)`
C. 50 `ms^(-1)`
D. 60 `ms^(-1)`

Answer

B

Explanation

From conversation of momentum, `m(v-10)=mv_(2)`
`v_(2)=(v-10)`
The coefficient of restitution, `e=("Velocity of separation")/("Velocity of approach")`
`=(v_(2)-v_(1))/(u_(1)+u_(2))=((v-10)-0)/((v+10))Rightarrow0.6=(v-10)/(v+10)`
`Rightarrow0.6v+6=v-10Rightarrow0.4v=16Rightarrowv=40ms^(-1)`