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A body of mass 4 m 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 υ . The total kinetic energy generated due to explosion is:

Options

  1. Am υ 2
  2. B3 2 m υ 2
  3. C2 m υ 2
  4. D4 m υ 2

Correct answer

B. 3 2 m υ 2

Step-by-step solution

The total momentum of the system will be conserved before and after explosion. Then, p i = p f O = m v i ^ + m v j ^ + 2 m v → v → = - v 2 i ^ - v 2 j ^ v → = v 2 Total kinetic energy generated due to explosion is K E = v 2 m v 2 + v 2 m v 2 + v 2 2 m v 2 2 = m v 2 + m v 2 2 = 3 2 m v 2

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