Question

A solid sphere of radius r/2 is cut out of a solid sphere of radius r such that the spherical cavity so formed touches the surface onone side and the center of the sphere on the other side as shown the initial mass of solid was m if a partical of mass m is placed at a distance 2.5r from the center of cavity then what is the gravitational attract on mass m

Answer 1

A solid sphere of radius r/2 is cut out of a solid sphere of radius

r such that the spherical cavity so formed touches the surface on one side

and the center of the sphere on the other side as shown the initial mass of

solid was m if a partical of mass m is placed at a distance 2.5r from the center of cavity then what is the gravitational attract on mass m

mass of extracted part from gravity

m`=M(4/3)π*(R/2)^3/(4/3)πR^3=M/8

using principle of superposition .

net force=GMm/(2R)^2-G(M/8)m/(2.5R)^2

              =23/100 GMm/R^2

hope it is helpful.