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

Solution

## The correct option is B The boat moves by $$0.4$$ mLet 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 mPhysics

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