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A body of mass (4m) is lying in xy-plane...

A body of mass (4m) 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 speeds (v). The total kinetic energy generated due to explosion is

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The correct Answer is:
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`2mv'costheta =mv` …………i
`impliessintheta=costheta=1/(sqrt(2))`

Putting this value in eqn i we get
`(2mv')/(sqrt(2))=mvimpliesv'=v/(sqrt(2))`
total `KE=1/2mv^(2)+1/2mv^(2)+1/2(2m)(v/(sqrt(2)))^(2)`
`=1/2mv^(2)+1/2mv^(2)+(mv^(2))/2=3/2mv^(2)`
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