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

Answer

`(1)`

Explanation

Total initial energy of two particles
`1/2(m_(1)u_(1)^(2)) + 1/2(m_(2)u_(2)^(2)) `
Total final energy of two particles
` = 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)) + varepsilon`
`therefore 1/2(m_(1)u_(1)^(2) + 1/2(m_(2)u_(2)^(2) - varepsilon = 1/2(m_(1)v_(1)^(2) + 1/2(m_(2)v_(2)^(2))`