A particle of mass `4 m` which is at rest explodes into masses `m, m` & `2m`. Two of the fragments of masses m and `2m` are found to move with equal speeds v each in opposite directions. The total mechanical energy released in the process of explosion is :-

Answer

`(3/2 mv^2)`

Explanation

`2 mv' cos theta = mv " "…..(i)`
`2 mv' sin theta = m v`
`implies sin theta = cos theta = 1/(sqrt2)`
Putting this value in Eq. (i) we get
`(2m v')/(sqrt2) = mv implies v' = v/(sqrt2)`
Total KE = `1/2 m v^2 + 1/2 mv^2 + 1/2 (2m) ((v)/(sqrt2))^(2)`
`=1/2 mv^2 + 1/2 mv^2 + (m v^2)/2 = 3/2 mv^2` .