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Question

A dumbbell is composed of two spheres that are connected by a rod whose mass is negligible. The distance between the centers of each sphere is d. One of the spheres has a mass of 2M and the mass of the other sphere is unknown, as shown.
If the dumbbell can balance when supported at a point 2d/3 from the center of the 2M sphere, what is the mass of the second sphere?
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A
2M
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B
3M
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C
22M
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D
4M
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E
5M
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Solution

The correct option is A 4M
Point C represents the centre of mass of the system i.e x=2d3
Given : m1=2M
Using x=m1x1+m2x2m1+m2

2d3=(2M)×0+m2d2M+m2

OR 4dM+2dm2=3dm2 m2=4M

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