A man of mass m stands on a long flat car of mass M, moving with veloc

1.	A man of mass m stands on a long flat car of mass M, moving with velocity V. If he now begins to run with velocity u, with respect to the car, in the same direction as V, the velocity of the car will be(a) V - mu/M (b) V - mu/(m + M) (c) V + mu/(m + M) (d) V - u(M - m)/(M + m)
Answer» Correct Answer is: (b) V - mu/(m + M) Momentum of the ‘man + car’ system = (m + M)V = constant. When the man begins to run, let v_M = velocity of man and v_C = velocity of car. ∴ velocity of man with respect to the car = u = v_M - v_C. By conservation of momentum, (m + M) V = mv_M + Mv_C. Rearranging, v_C = V - mu/m + M.

A man of mass m stands on a long flat car of mass M, moving with velocity V. If he now begins to run with velocity u, with respect to the car, in the same direction as V, the velocity of the car will be(a) V - mu/M (b) V - mu/(m + M) (c) V + mu/(m + M) (d) V - u(M - m)/(M + m)

Answer»

Correct Answer is: (b) V - mu/(m + M)

Momentum of the ‘man + car’ system = (m + M)V = constant. When the man begins to run, let v_M = velocity of man and v_C = velocity of car.

∴ velocity of man with respect to the car = u = v_M - v_C.

By conservation of momentum, (m + M) V = mv_M + Mv_C.

Rearranging, v_C = V - mu/m + M.

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A man of mass m stands on a long flat car of mass M, moving with velocity V. If he now begins to run with velocity u, with respect to the car, in the same direction as V, the velocity of the car will be(a) V - mu/M (b) V - mu/(m + M) (c) V + mu/(m + M) (d) V - u(M - m)/(M + m)

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