Two particle of masses `m_(1).m_(2)` moves with initial velocities `u_(1) and u_(2)` . On collision one of the particles get excited to higher level after absorbing energy `epsilon` . If final velocities of particles be `v_(1) and v_(2)` then we must have :

Options

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

Answer

B

Explanation

Energy is always be conserved so
`K.E_("intial")=K.E_("final") +` Excitation energy
`1/2 m_(1)u_(1)^(2)+1/2m_(2)u_(2)^(2)-epsilon =1/2m_(1)v_(1)^(2)+1/2m_(2)v_(2)^(2)`