At what altitude will the acceleration due to gravity be `25%` of that at the earth's surface (given radius of earth is `R`)?

Options

A. `R//4`
B. R
C. `3R//8`
D. `R//2`

Answer

B

Explanation

`g=(GM)/(r^(2)) rArr g_(0)=(GM)/(R^(2))` ..(i)
`g_(h)=(GM)/((R+h)^(2))` …..(ii)
`(g_(h))/(g_(0))=((R )/(R+h))^(2) rArr (1)/(4)=((R )/(R+h))^(2) rArr (R )/(R+h)=(1)/(2)`
`R+h =2R rArr h=R`