Question

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

Correct Answer - A::B
For `rgtR,` the gravitational field is `F=GM//r^(2)`
`:. F_(1)=(GM)/(r_(1)^(3))` and `F_(2)=(GM)/(r_(2)^(2))implies(F_(1))/(F_(2))=(r_(2)^(2))/(R_(1)^(2))`
For `rgt gtR`
The gravitational field is `F=(GM)/(R^(3))xxr`
`:. F_(1)=(GM)/R^(3)xxr_(1)` and `F_(2)=(GM)/(R^(3))xxr_(2)`
`implies (F_(1))/(F_(2))=(r_(1))/(r_(2))`