If a body of mass m moving with velocity v collides with another body of mass m at rest. If e is the coefficient of restitution then find the ratio of final velocities of two bodies :

Options

A. `(v_(1))/(v_(2))=(1-e)/(1+e)`
B. `(v_(1))/(v_(2))=(1+e)/(1-e)`
C. `(v_(1))/(v_(2))=e`
D. None of these

Answer

a

Explanation

According to conservation of linear momnetum,
`mv+0=mv_(1)+mv_(2)`
`implies v_(1)+v_(2)=v` ….(i)
Also `e=(v_(2)-v_(1))/(u_(1)-u_(2))` implies `e=(v_(2)-v_(1))/(v-0)`
`implies v_(2)-v_(1)=ev` ...(ii)
Adding (i) and (ii)
`2v_(2)=v+ev`.
`v_(1)=(1+e)v/2` ...(iii)
Subtracting (ii) from (i)
`2v_(1)=v-ev`
`v_(1)=(1-e)v/2`
Dividing (iv) by (iii),
`:.(v_(1))/(v_(2))=(1-e)/(1+e)`