The magnitude of the gravitational field at distance `r_1 and `r_2` from the centre of a unifrom 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_1gt R and r_2 gtR`
C. `(F_1)/(F_2) = (r_1)/(r_2) if r_1 gtR and r_2 gtR`
D. `(F_1)/(F_2) = (r_1^2)/(r_2^2) if r_1 ltR and r_2 ltR`

Answer

A, B

Explanation

(a,b) `For rgt R, the gravitational field is F = (GM)/(r^2)`
`:.F_1 = (GM)/(r_1^2) and F_2 = (GM)/(r_2^2) rArr (F_1)/(r_2^2)/(r_1^2)`
For rltR, the gravitational field is `F = (GM)/(R^3)xxr`
`:.F_1 = (GM)/(R^3) xxr_1 and F_2 = (GM)/(R^3)xxr_2`
`rArr (F_1)/(F_2) - (r_1)/(r_2)`