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`,are `(I_(1))` and `(I_(2))` respectively. Find the ratio of `(I_(1))//(I_(2)))` if `r_(1)gtR` and `r_(2)ltR`.

Options

A. `(F_(1))/(F_(2))=(r_(1))/(r_(2))lif r_(1) lt R and r_(2)ltR`
B. `(F_(1))/(F_(2))=(r_(1)^(2))/(r_(2)^(2)),if r_(1) gt R and r_(2)gt R`
C. `(F_(1))/(F_(2))=(r_(2))/(r_(1)), ifr_(1)lt R and r_(2) lt R`
D. `(F_(1))/(F_(2))=(r_(2)^(2))/(r_(1)^(2)), if r_(1)gtR and r_(2)lt R`

Answer

A

Explanation

As, `g=(4)/(3)pi rhoGr`
`:. g prop r if r lt R`
`g=(GM)/(r^(2))`
`:. g prop (1)/(r^(2))if r gtR`
If `r_(1) lt R and r_(2) lt R`, then `(F_(1))/(F_(2))=(g_(1))/(g_(2))=(r_(1))/(r_(2))`
If `r_(1)gt R and r_(2)gt R`, then `(F_(1))/(F_(2))=(g_(1))/(g_(2))=((r_(2))/(r_(1)))^(2)`.