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Question

A uniform sphere of mass M and radius R exerts a force F on a small mass m situated at a distance of 2R from the centre O of the sphere. A spherical portion of diameter R is cut from the sphere as shown in the figure. The force of attraction between the remaining part of the sphere and the mass m will be

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Solution

The correct option is **A**

7F9

The force of attraction between the complete sphere and mass m is

F=GmM(2R)2=GmM4R2

Mass of complete sphere is M=4π3R3ρ, where ρ is the density of the sphere.

Mass of the cut-out portion is m0=4π3(R2)2ρ=M8.

Now, the distance between the centre of the cut out portion and mass m =2R−R2=3R2

Hence, the force of attraction between the cut out portion and mass m is f=Gm0m(3R2)2=G(M8)m9R24=GmM4R2×29=2F9

Therefore, the force of attraction between the remaining part of the sphere and mass m =F−f=F−2F9=7F9 which is choice (a).

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