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Question: Answered & Verified by Expert
A solid sphere of uniform density and radius r applies a gravitational force of attraction equal to F1on a particle placed at P, distance 2R from the centre O of the sphere. A spherical cavity of the radius R2 is now made in the sphere as shown in the figure. The sphere with cavity now applied a gravitational force F2 on the same particle placed at P. The ratio F2F1 will be

PhysicsGravitationJEE Main
Options:
  • A 12
  • B 79
  • C 3
  • D 7
Solution:
1050 Upvotes Verified Answer
The correct answer is: 79
Gravitational force due to solid sphere, F 1 = G M m 2 R 2 ,
where M and m are mass of the solid sphere and particle respectively and R is the radius of the sphere. The gravitational force on particle due to sphere with cavity = force due to solid sphere creating cavity, assumed to be present above at that position

i.e., F2=GMm4R2=GM/8m3R/22=736GMmR2

So, F2F1=7GMm36R2/GMm4R2=79

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