A ball collides impinges directly on a similar ball at rest. The first ball is brought to rest after the impact. If half of the kinetic energy is lost by impact, the value of coefficient of restitution `( e)` is

Options

A. `1/2`
B. `1/sqrt(3)`
C. `1/sqrt(2)`
D. `(sqrt(3))/2`

Answer

A

Explanation

`m_(1)v_(1) =m_(2)v_(2)`
`1/2mv_(2)v_(2)^(2)=1/2[1/2m_(1)u_(1)^(2)]`
`implies (m_(2)v_(2))=1/2(m_(1)u_(1))impliesv_(2)=u_(1)/2`
`e=(v_(2)-v_(1))/(u_(1)-u_(2))=(v_(2)-0)/(u_(1)-0)=v_(2)/u_(1)impliese=1/2`