A particle of mass `m` travelling with velocity `v` and kinetic energy `E` collides elastically to another particle of mass `nm`, at rest. What is the fraction of total energy retained by the particle of mass `m`?

Options

A. `((n+1)/n)^(2)`
B. `((n+1)/(n-1)^(2))`
C. `((n-1)/(n+1))^(2)`
D. none of these

Answer

C

Explanation

`mv=mv_(1)+nmv_(2)`
`v=v_(1)+mv_(2)=v_(2)v_(1)`
`implies v_(2)=(2v)/((n+1)),v_(1)=((1-n)/(1+n))v`
`(KE_(1))/(KE_(2))=(1/2mv_(1)^(2))/(1/2mv^(2))=((1-1)/(n+1))^(2)`