The magnitude of gravitational field at distances `r_(1)` and `r_(2)` from the centre of a uniform sphere of radius `R` and mass `M`, respectively. Find the ratio of `(I_(1))//(I_(2)))` if `r_(1)gtR` and `r_(2)gtR`.

Explanation

When `r_(1)gtR`, the point lies outside the sphere. Then sphere can be considered to be a point mass body whose whole mass can be supposed to be concentrated at its centre. The gravitational intensity at a point distance `r_(1)` from the centre of sphere will be
`I_(1)=GM/(r^(3))`.............i
When` r_(2)ltR`, the point `P` lies inside the sphere. The unit mass body placed at `P` will experiences gravitational pull due to sphere of radius `r_(2)` whose mass is
`M=(Mxx4/3pir_(2)^(3))/(4/3piR^(3))=(Mr_(2)^(3))/(R^(3))`
Therefore the gravitational intensity at `P` will be
`I_(2)=(GMr_(2)^(3))/(R^(3))xx1/(r_(2)^(2))=(GMr^(2))/(R^(3))`............ii
So, `(I_(1))/(I_(2))=(GM)/(r_(1)^(2))xx(R^(2))/(GMr_(2))=(R^(3))/(r_(1)^(2)r_(2))`