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A metal ball of mass 2 kg moving with a velocity of 36 km/h has a head on collision with a stationary ball of mass 3 kg. If after the collision, the two balls move together, the loss in kinetic energy due to collision is

  1. 140 J
  2. 100 J
  3. 60 J
  4. 40 J

Correct answer: 140 J

Solution

The initial kinetic energy of the system is due to the moving 2 kg ball: KE_initial = (1/2) * 2 * (10)^2 = 100 J (converting 36 km/h to 10 m/s). After the collision, the combined mass (5 kg) moves with velocity v = (2 * 10) / (2 + 3) = 4 m/s. The final kinetic energy is KE_final = (1/2) * 5 * (4)^2 = 40 J. The loss in kinetic energy is KE_initial - KE_final = 100 - 40 = 60 J.

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