Two particles of masses `m_(1),m_(2)` move with initial velocities `u_(1)` and `u_(2)`. On collision, one of the particles get excited to higher level, after absording enegry. If final velocities of particles be `v_(1)` and `v_(2)` then we must have

Options

A. `m_(1)^(2)u_(1)+m_(2)^(2)u_(2)^(2)-epsi=m_(1)^(2)v_(1)+m_(2)^(2)v_(2)`
B. `1/2m_(1)u_(1)^(2)+1/2m_(2)u_(2)^(2)=1/2m_(1)v_(1)^(2)+1/2m_(2)v_(2)-epsi`
C. `1/2m_(1)u_(1)^(2)+1/2m_(2)u_(2)^(2)-epsi=1/2m_(1)v_(1)^(2)+1/2m_(2)v_(2)`
D. `1/2m_(1)u_(1)^(2)+1/2m_(2)u_(2)^(2)+epsi=1/2m_(1)v_(1)^(2)+1/2m_(2)v_(2)`

Answer

c

Explanation

(c )Total intial energy`=(1)/(2)m_(1)u_(1)^(2)+1/(2)m_(2)u_(2)^(2)`
Since, after collision one particle absorn energy `epsi`
`therefore` Total final energy `=(1)/(2)m_(1)v_(1)^(2)+1/(2)m_(2)v_(2)^(2)+epsi`
From conservation of energy,
`(1)/(2)m_(1)u_(1)^(2)+1/(2)m_(2)u_(2)^(2)=(1)/(2)m_(1)v_(1)^(2)+1/(2)m_(2)v_(2)^(2)+epsi`
`implies(1)/(2)m_(1)u_(1)^(2)+1/(2)m_(2)u_(2)^(2)-epsi=(1)/(2)m_(1)v_(1)^(2)+1/(2)m_(2)v_(2)^(2)`