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

Answer

C

Explanation

`u_(1)=2 m//s " "u_(1)=0`
`m_(1)=m " "m_(2) = 2m `
`e = (v_(2)-v_(1))/((u_(2)-u_(1)))`
`0.5 = (v_(2)-v_(1))/2 `
`v_(2) - v_(1) = 1m//s " " …(i)`
`m_(1)u_(1)+m_(2)u_(1)=m_(1)v_(1)+m_(1)v-(2) `
`m(2) + 0 = mv_(1)+2mv_(2)`
`v_(1) +2v_(2) = 2m//s " " `...(ii)
Solve equation (i) and (ii)
`3v_(2)=3`
`v_(2)=1 ` m/s
`v_(1)=0` m/s