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Question

# A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F1 on a particle placed at P, distance 2R from the centre O of the sphere. A spherical cavity of radius R/2 is now made in the sphere as shown in figure. The sphere with cavity now applies a gravitational force F2 on same particle placed at P. The ratio F2F1 will be

A

1/2

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B

7/9

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C

3

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D

7

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Solution

## The correct option is B 7/9 F1 = G43πr3ρm4r2 = 13 π ρ Gm R F2 = G43πr3ρm4r2 - G43πr38ρm94R2 = 13 π ρ GmR - 227 π ρ Gm R ∴ F1F2 = 1313−227 = 11−29 = 97 → F1F2 = 79

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