From a sphere of mass M and radius R a smaller sphere of radius R/2 is carved out such that the cavity made in the original sphere is between its centre and the periphery.For the configuration in the above mentioned case where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two sphere is:

Question

From a sphere of mass M and radius R a smaller sphere of radius R/2 is carved out such that the cavity made in the original sphere is between  its centre and the periphery.For the configuration in the above mentioned case  where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two sphere is:

irishboy123 · Answer

i think you should use superposition

so calculate it as (A) the force that would have been on the R/2 sphere from a complete sphere of rad R; Minus (B) the force you would get  on the R/2 sphere from a sphere the size of the cavity only, ie also rad R/2

which involves the same steps as recalculating the centre of mass of the larger sphere....which makes sense

priyar · Answer

thanks for the help!

priyar · Answer

i tried using your method but did not get the correct answer..the mass of the smaller sphere is M/8 right?

priyar · Answer

I am getting 7G(M^2)/72(R^2)..but that's not the answer..

priyar · Answer

i got the answer! i had made a small mistake..