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JEE MainPhysicsCenter of Mass, Momentum and Collision

A shell of mass M moving with initial speed V explodes into fragments. The total kinetic energy of the system immediately after the explosion is given as n times its initial kinetic energy. The kinetic energy of the fragments relative to the center of mass immediately after the explosion is

Options

  1. A1 2 (n-1)MV^2
  2. B1 2 nMV^2
  3. C1 2 (n+1)MV^2
  4. D(n-1)MV^2

Correct answer

A. 1 2 (n-1)MV^2

Step-by-step solution

The initial kinetic energy of the shell is: K_ initial = 1 2 MV^2 Since the explosion is caused by internal forces, the velocity of the center of mass remains unchanged. Therefore, the kinetic energy of the center of mass after the explosion is still: K_ cm = 1 2 MV^2 The total kinetic energy immediately after the explosion is given as n times the initial kinetic energy: K_ total = n 1 2 MV^2 According to Koenig's theorem, the total kinetic energy of a system is the sum of the kinetic energy of the center of mass a

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