Work, Energy And Power

Question

A body of mass (4m) is lying in x-y 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,

mv²

$3 over 2 m v squared$

2mv²

4 mv²

Solution

3 over 2 m v squared

As per the question, the third part of mass 2m will move because the total momentum of the system after explosion must remain zero.

Let the velocity of the third part be v'.
According to the law of conservation of momentum,

space space space space square root of 2 space left parenthesis m v right parenthesis space equals space left parenthesis 2 m right parenthesis space x space v apostrophe rightwards double arrow space space space space v apostrophe space equals space fraction numerator v over denominator square root of 2 end fraction

Total kinetic energy generated by the explosion,

equals space 1 half mv squared space plus space 1 half mv squared space plus space 1 half space left parenthesis 2 straight m right parenthesis space straight v apostrophe squared

equals space mv squared space plus space mv squared over 2 equals space 3 over 2 mv squared

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