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Question

Two men, of masses $$60$$ kg and $$80$$ kg are sitting at the ends of a boat of mass $$60$$ kg and length $$4$$ m. The boat is stationary. If the men now exchange their positions, then?


A
The centre of mass of the two men shifts by 2 m
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B
The boat moves by 0.4 m
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C
The centre of mass of the two men shifts by 4/7 m
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D
The boat moves by 0.6 m
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Solution

The correct option is B The boat moves by $$0.4$$ m
Let X be the center of mass from 60 kg, assuming torque at X
$$60X=60(2-X)+80(4-X)$$
$$60X=120X-60X+320-80X$$
$$200X=440$$
$$X=\dfrac{11}{5}$$
Similarly when they interchange their position with each other
$$80X=60(2-X)+60(4-X)$$
$$80X=120-60X+240-60X$$
$$200X=360$$
$${X}_{inetr}=\dfrac{9}{5}$$
Thus by interchanging their position the center of mass shifts 
  $${X}_{shift}=\dfrac{11}{5}-\dfrac{9}{5}$$=$$\dfrac{2}{5}$$=0.4 m

Physics

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