Two men of mass 60 kg and 80 kg stand on a plank of mass 20 kg. Both of them can jump with a velocity of 1 m/s relative to the plank. In each event shown in List-I, find the velocity of the plank afte

Question

Two men of mass 60 kg and 80 kg stand on a plank of mass 20 kg. Both of them can jump with a velocity of 1 m/s relative to the plank. In each event shown in List-I, find the velocity of the plank after the event.

List-I	List-II
(P) Ram alone jumps to the left	$(1) - \frac{17}{40} m/s$
(Q) Shyam alone jumps to the right	$(2) - \frac{1}{2} m/s$
(R) Ram jumps to left and Shyam jumps to right simultaneously.	$(3) \frac{3}{8} m/s$
(S) Ram jumps to left and after that Shyam jumps to right.	$(4) - \frac{1}{8} m/s$
	$(5) - \frac{2}{3} m/s$

TestHub · Accepted Answer

Take the rightward direction as positive. The system is initially at rest.

P: Ram jumps left at 1 m/s relative to the plank.

$60 (V - 1) + 100 V = 0$

$V = \frac{3}{8} m/s$

Q: Shyam jumps right at 1 m/s relative to the plank.

$80 (V + 1) + 80 V = 0$

$V = - \frac{1}{2} m/s$

R: both jump simultaneously.

$60 (V - 1) + 80 (V + 1) + 20 V = 0$

$V = - \frac{1}{8} m/s$

S: after Ram jumps, Shyam and the plank move at 3/8 m/s. Apply momentum conservation to Shyam and the plank during the second jump.

$100 (\frac{3}{8}) = 80 (V + 1) + 20 V$

$V = \frac{3}{8} - \frac{4}{5} = - \frac{17}{40} m/s$

P to 3, Q to 2, R to 4, S to 1. Answer: B.

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