The mass of a satellite is `M//81` and radius is `R//4` where `M` and `R` are the mass and radius of the planet. The distance between the surfaces of planet and its satellite will be atleast greter than:

Options

A. `1.25R`
B. `12.5R`
C. `10.5R`
D. `5R`

Answer

A

Explanation

At `P` gravitational pull is same
`(GMm)/((R+x)^(2))=(GMm)/(g_(1)(R/4+y)^(2))`
`(R+x)^(2)=81(R/4+y)^(2)=[9(R/4+y)]^(2)`
`R+x=9(R/4+y)` Let `x+y=r`
From (1) ` R+(r-y)=9(R/4+y)`

`y=1/10[r-5/4R]`
Since `ygt0, rgt5/4R` (at least)