The magnitudes 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 `E_(1)` and `E_(2)` respectively. Then:

Options

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

Answer

A

Explanation

If `r le R` then `E=(GM)/(R^(3))(r)impliesE oo r`
`implies(E_(1))/(E_(2))=(r_(1))/(r_(2))` if `r_(1)ltR ` and `r_(2)ltR`
If `rgeR`, then `E=(GM)/(r^(2))implies E oo 1/(r^(2))`
`implies(E_(1))/(E_(2))=(r_(2)^(2))/(r_(1)^(2))` if `r_(1)gtR ` and `r_(2)gtR`