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The magnitudes of the gravitational forc...

The magnitudes of the gravitational force at distances `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 (more than one are correct)

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`

Text Solution

Verified by Experts

The correct Answer is:
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))`
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