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 speeds $$($$ν$$)$$. The total kinetic energy generated due to explosion is

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 speeds $$($$ν$$)$$. The total kinetic energy generated due to explosion is

Infinity Learn · Accepted Answer

Let v→′be velocity of third piece of mass $$2$$ m. Initial momentum, p→$$i=0(As$$ the body is at $$rest)Final$$ momentum, p→$$f=mv$$ı$$^+mv$$ȷ$$^+2mv$$→′ According to law of conservation of momentum p→$$i=p$$→$$f0=mvi^+mvj^+2mv$$→′v→′$$=$$−$$v2i^$$−$$v2j^$$ The magnitude of v→′ is v'$$=$$−$$v22+$$−$$v22=v2$$ Total kinetic energy generated due to explosion $$=12mv2+12mv2+12(2m)v$$′$$2=12mv2+12mv2+12(2m)v22=mv2+mv22=32mv2$$

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 speeds ( $ν$ ). The total kinetic energy generated due to explosion is

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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 speeds (ν). The total kinetic energy generated due to explosion is

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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 speeds ( $ν$ ). The total kinetic energy generated due to explosion is