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

Answer

C

Explanation

`KE_("Before collision") = (1)/(2)m_(1)u_(1)^(2) + (1)/(2)m_(2)u_(2)^(2)`
`KE_("After collision") = (1)/(2)m_(1) upsilon_(1)^(2) + (1)/(2)m_(2)upsilon_(2)^(2)`
` = (1)/(2)m_(1)u_(1)^(2) + (1)/(2)m_(2)u_(2)^(2) - epsilon`
`KE_("Before collision") = KE_("After collision")`
`(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)`