A ball moving with velocity `2 ms^(-1)` collides head on with another stationary ball of double the mass. If the coefficient of restitution is `0.5`, then their velocities (in `ms^(-1)`) after collision will be

Options

A. `0,2`
B. `0,1`
C. `1,1`
D. `1,0.5`

Answer

B

Explanation

Here, `u_(1)=2 m//s, u_(2)=0, e=0.5,`
`m_(1)=m, m_(2)=2m`
As momentum is conserved
`:. m_(1)u_(1)+m_(2)u_(2)=m_(1)upsilon_(1)+m_(2)upsilon_(2)`
` mxx2+2 mxx0=m upsilon_(1)+2 m upsilon_(2)`
or `upsilon_(1)+2 upsilon_(2)=2 ....(1) `
As coefficient of restitution `e=(upsilon_(2)-upsilon_(1))/(u_(1)-u_(2))`
`0.5=(upsilon_(2)-upsilon_(1))/(2-0)` or `upsilon_(2)-upsilon_(1) ......(ii)`
Adding `(i)` and `(ii)`
`3 upsilon_(2)=3` or `upsilon_(2)=1 m//s`
`upsilon_(1)=0 m//s`