A body of mass (4m) is laying in xy-plane at rest. It suddenly explodes into three pieces. Two pieces each mass (m) move perpedicular to each other with equal speeds (v). Total kinetic energy generated due to explosion is

Options

A. `mv^(2)`
B. `3/2 mv^(2)`
C. `2 mv^(2)`
D. `4mv^(2)`

Answer

`(2)`

Explanation

Let `vec v` be velocity of third piece of mas 2m. Initial momentum, `vec p_(i) = 0` (as the body is at rest) Final momentum, ` vec P _(f) = m v hat i + mv hat j + 2 m vec v`
According to law of conservation of momentum ` vec P_(i) = vec P_(f)`
`0 = mv hat i + mv hat j + 2m vec v`
`vec v = -v/2 hat i - v/2 hat j`
The magnitude of v. is
`v. = sqrt((-v/2)^(2) + (-v/2)^(2)) = v/sqrt 2`
Total kinetic energy generated due to explosion
`1/2 mv^(2) + 1/2 mv^(2) + 1/2(2m)v^(2)`
` = 1/2 mv^(2) + 1/2 mv^(2) + 1/2(2m)((v)/(sqrt 2))^(2)`
` = mv^(2) + (mv)^(2)/2 = 3/2 mv^(2)`