A body of mass 4 m is lying in xy - plane at rest. It suddenly explodes into three pieces. Two pieces each of mass m move perpendicular to each other with equal speed v. The total kinetic energy generated due to explosion is

Options

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

Answer

B

Explanation

Initial momentum `P_(i)=vec0`
Findal momentu `P_(f)=0`
But `P_(f)=mvecv_(i)+mvecv_(f)+vecP_(3)=0`
`P_(3)=mvsqrt(2)`
Total K.E. = `(P_(3)^(2))/(2xx2m)+(1)/(2)mv^(2)+(1)/(2)mv^(2)`
`=(2m^(2)v^(2))/(4m)+mv^(2)`
`=(3mv^(2))/(2)[P_(3)=mv]`