First slide

Motion of centre of mass

Question

A boat of mass 80 kg is floating on still water. A dog of mass 20 kg on the boat is at a distance of 10m from the shore. The dog moves on the boat by a distance of 2m towards the shore. The distance of the dog from the shore is

Moderate

A

11.6m
B

8.4m
C

9.6m
D

10.4m

Solution

distance of dog from shore $\large \left\{ { = d - x + \frac{{mx}}{{m + M}}} \right.$
$\large = 10 - 2 + \frac{{20\left( 2 \right)}}{{20 + 30}} = 8 - \frac{2}{5} = 8.4m$
Alternative Solution:
Position of centre of the system remains fixed. If x be the displacement of the boat away from the shore, then using $\large (M+m)\times \Delta x_c=Mx+m(x-2)$
$\large \Rightarrow x=\frac {2m}{M+m}=\frac {2\times 20}{80+20}=0.4m$
$\large \therefore$ distanc of dog = (10+ 0.4 - 2)m = 8.4m

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