The magnitude of the gravitational field at distance `r_(1)` and `r_(2)` from the centre of a uniform sphere of radius `R` and mass `M` are `F_(1)` and `F_(2)` respectively. Then:

Options

A. `(F_(1))/(F_(2))=(r_(1))/(r_(2))` if `r_(1)ltR` and `r_(2)ltR`
B. `(F_(1))/(F_(2))=(r_(2)^(2))/(r_(1)^(2))` if `r_(1)gtR` and `r_(2)gtR`
C. `(F_(1))/(F_(2))=(r_(1)^(3))/(r_(2)^(3))` if `r_(1)ltR` and `r_(2)ltR`
D. `(F_(1))/(F_(2))=(r_(1)^(2))/(r_(2)^(2))` if `r_(1)ltR` and `r_(2)ltR`

Answer

A, B

Explanation

Gravitational field intensity `F=(GMr)/(R^(3))`
Inside the sphere
`(F_(1)propr_(1),F_(2)propr_(2))`
`(F_(1))/(F_(2))=(r_(1))/(r_(2))` or `r_(1)ltR&r_(2)ltR`
Gravitational field intensity
`Iprop(1)/(r^(2))` (out side the sphere)
`therefore(F_(1))/(F_(2))=(r_(2)^(2))/(r_(1)^(2))` if `r_(1)gtR` and `r_(2)gtR`