JEE Advanced 2010 Physics question

A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 . Which of the following statement(s) is (are) correct for the system of these two masses ?

(A)Total momentum of the system is 3 kg Correct
(B)Momentum of 5 kg mass after collision is 4 kg
(C)Kinetic energy of the centre of mass is 0.75 JCorrect
(D)Total kinetic energy of the system is 4 J

Answer: (A),(C)

Solution

Let the 1 kg mass have initial velocity u and let the final velocities be (reversed) and . Momentum conservation: . Elastic collision (velocity of separation = velocity of approach): . Solving: $ + 2 = -2 + ⇒

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Question ID VK-025800