Two masses, `m_(1)` and `m_(2)` , are moving with velocities `v_(1)` and `v_(2)`. Find their total kinetic energy in the reference frame of centre of mass.

Explanation

`K=1/2m_(1)v_(1c)^(2)+1/2m_(2)v_(2c)^(2)`………..i
where `v_(1c)` and `v_(2c)` are velocities relatives to the `CM`
`v_(1c)=v_(1)-v_(cm)=v_(1)-((m_(1)v_(1)+m_(2)v_(2))/(m_(1)+m_(2)))=(m_(2)(v_(1)-v_(2)))/(m_(1)+m_(2))`
`v_(2c)=v_(2)-v_(CM)=v_(2)-((m_(1)v_(1)+m_(2)v_(2))/(m_(1)+m_(2)))=(m_(1)(v_(2)-v_(1)))/(m_(1)+m_(2))`
putting these eqn i `K=1/2(m_(1)m_(2))/((m_(1)+m_(2)))(v_(1)-v_(2))^(2)`