A solid sphere of uniform density and radius r

Asked by admin @ 13/08/2021 in Physics viewed by 371 People

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?

Answered by admin @ 13/08/2021

Here is your answer ⤵⤵⤵

Let us assume the mass of sphere as M.

First find out the force by the intact sphere by F1=GMm4R2

To find F2, divide the cavity sphere into 2 spheres of positive mass and a negative mass, like we do in all cavity problems.

Find out the mass of negative sphere= M/8 ( as the density is same, mass will depend on the volume)

after this we find out the forces by these 2 spheres of masses M, -M/8 at a distance of 2R, 3R/2 respectively, and add them.

F2= GMm(2R)2+G−M8m(3R2)2

find F2/F1= 7/9

HOPE IT HELPS YOU ☺☺ !!!

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A solid sphere of uniform density and radius r

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