A particle of mass `4m` which is at rest explodes into four equal fragments. All four fragments scattered in the same horizontal plane. Three fragments are found to move with velocity `v` as shown in the figure. The total energy released in the process is

Options

A. `mv^(2) (3 - sqrt2)`
B. `mv^(2) (3 - sqrt2)2`
C. `2mv^(2)`
D. `mv^(2) (1 + sqrt2)2`

Answer

A

Explanation

` COLM rArr mvhat(i) + mvhat(j) + m ((-v)/(sqrt2)hat(i) - (v)/(sqrt2)hat(j)) + mv_(4) = 0`
`vec(v)_(4) = -v (1 - (1)/(sqrt2)) hat(i) - v(1 - (1)/(sqrt2))hat(j)`

Total energy relased
`= (1)/(2)mv^(2) + (1)/(2)mv^(2) + (1)/(2)mv^(2) + (1)/(2)m[v^(2)(1 - (1)/(sqrt2))^(2) xx 2]`
`= mv^(2)(3 - sqrt2)`