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Question

A man of mass M=50 kg stands at one end of the boat which is floating on still water. The man walks to the other end of the boat. Length of the boat is L=10 m and mass M=100 kg. Then find the distance moved by the boat relative to the ground
  1. 23 m
  2. 0 m
  3. 53 m
  4. 103 m


Solution

The correct option is D 103 m
Here no external force is acting on the system. Hence xcom=0.
COM will not change its position.

Assume


When man reaches the other end boat moved x distance relative to the ground. 

Hence, 
Distance travelled by the man w.r.t ground,
x1=(Lx)=(10x) m 
Distance travelled by the boat w.r.t ground is x m
As we know,
Δxcom=m1Δx1+m2Δx2m1+m2
Δxcom=0
0=50×(10x)+(100)(x)50+100
(x because we assumed rightward movement as positive)
50050x100x=0
x=500150
x=103 m 

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