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. ` 2mv^2`
B. `4mv^2`
C. `mv^2`
D. `3/2 mv^2`

Answer

D

Explanation

`mv(hati) +mv(hatj)=2mv_s`
`implies v_3 = sqrt((v^2+v^2)/(2))=(sqrt2v)/2=v/sqrt2`
`KE=1/2 mv^2 +1/2 mv^2 +1/2 xx 2m xx (v/sqrt2)^2`
`=mv^2 +(mv^2)/2=3/2 mv^2`