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JEE Main202229 Jun 2022Morning ShiftPhysicsCenter of Mass, Momentum and CollisionActual

A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2 . Two smaller pieces fly off perpendicular to each other with velocities of 30 m s - 1 and 40 m s - 1 respectively. The velocity of the third piece will be

Options

  1. A35   m   s - 1
  2. B50   m   s - 1
  3. C25   m   s - 1
  4. D15   m   s - 1

Correct answer

C. 25   m   s - 1

Step-by-step solution

Let the masses of the three parts be m ' ,   m ' and 2 m ' . Momentum of first part p 1 = m ' × 30 = 30 m ' and momentum of second part p 2 = m ' × 40 = 40 m ' . Third part will fly in a direction opposite to the direction of resultant of p 1 and p 2 , so that total momentum of the system after explosion remains zero. Momentum of the third part is p 3 = p 1 2 + p 2 2 = 30 m ' 2 + 40 m ' 2 = 50 m ' Velocity of third part, v = 50 m ' 2 m ' = 25   m &

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