Two identical particles collide in air inelastically. One moves horizontally and the other moves vertically with equal speed just before collision. The fractional loss in kinetic energy of the system of particles is equal to

Options

A. `1/sqrt(2)`
B. `1/2`
C. `sqrt(3)/2`
D. none of these

Answer

B

Explanation

Conservation of linear mometum yields
`mvhati+mvhatj=(2m)vecv`

`impliesvecv'=v/2(hati+hatj)=v'=v/sqrt(2)`
`eta=1-(KE_(f))/(KE_(i))=1-((1//2)(2m)v^('2))/((1//2)mv^(2)+(1//2)mv^(2))`
`implies eta=1-((v')/v)^(2)=1-(1/sqrt2)^(2)=1/2`