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 absorbing enegry. If final velocities of particles be `v_(1)` and `v_(2)` then we must have

Options

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

Answer

B

Explanation

As energy is conserved,
`:. KE_(i nitial)=KE_(fi nal)+` Excitation Energy
`(1)/(2)m_(1)u_(1)^(2)+(1)/(2)m_(2)u_(2)^(2)=(1)/(2)m_(1)upsilon_(1)^(2)+(1)/(2)m_(2)upsilon_(2)^(2)+in`
or `(1)/(2)m_(1)u_(1)^(2)+(1)/(2)m_(2)u_(2)^(2)-in=(1)/(2)m_(1)upsilon_(1)^(2)+(1)/(2)m_(2)upsilon_(2)^(2)`