A solid sphere of uniform density and radius R apies a grav force of attraction =F1 on a particle placed - Physics - Gravitation

Question

A solid sphere of uniform density and radius R apies a grav
force of attraction =F1 on a particle placed at A distance of 2R
fro the centre of the sphere A spherical cavity of radius R/2 is
now made in the sphere which applies a force F2 on the same
particle, FI/F2?

Jyoti Pant · Accepted Answer

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Suppose the particle of mass m is placed on A
Then,F1=GMm(2R)2=GMm4R2If a spherical part of radius R/2 is taken out from the big sphere, then the mass of remaining sphere is=[4πR33-4π3(R2)3]×d=4πR33×(78)×d=7M8[Where, Mass=Volume ×densityM=4πR33×d]Now,Force on mass 'm' placed at A is given asF2=Force due to sphere-Force due to cavity=GMm4R2-GMm×48×9R2=74×GMm9R2F1F2=GMm4R2×4×9R27GMm=97Or F1:F2=9:7

A solid sphere of uniform density and radius R apies a grav force of attraction =F1 on a particle placed at A distance of 2R fro the centre of the sphere . A spherical cavity of radius R/2 is now made in the sphere which applies a force F2 on the same particle, FI/F2?