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The magnitude of the gravitational field...

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:

A

`F_1/F_2=r_1/r_2` if `r_1 lt R` and `r_2 lt R `

B

`F_1/F_2=r_2^2/r_1^2` if `r_1 gt R` and `r_2 gt R`

C

`F_1/F_2 = r_1/r_2` if `r_1 gt R` and `r_2 gt R`

D

`F_1/F_2=r_1^2/r_2^2` if `r_1 lt R` and `r_2 lt R `

Text Solution

Verified by Experts

The correct Answer is:
A, B
For r > R , the gravitational field is `F=GM//r^2`
`therefore F_1="GM"/r_1^2` and `F_2=(GM)/r_2^2 rArr F_1/F_2=r_2^2/r_1^2`
For r < R
The gravitational field is `F=(GM)/R^3 xxr therefore F_1=(GM)/R^3 xx r_1` and `F_2=(GM)/R^3 xx r_2 rArr`
`F_1/F_2=r_1/r_2`
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