Imagine earth to be a solid sphere of mass M and radius R. if the value of acceleration due to gravity at a depth d below earth's surface is same as its value at a height h above its surface and equal to `g/4` (where g is the value of acceleration due to gravity on the surface of earth ), the ratio of `h/d` will be

Options

A. 1
B. `4/3`
C. `3/2`
D. `2/3`

Answer

B

Explanation

At depth d below the earth.s surface,
`g/4=g(1-d/R)`
`or, d/R=1-1/4 or, d=3/4R`
At height h above the earth.s surface,
`g/4 =g(R/(R+h))^2 or, R/(R+h) =1/2`
`or, R+h=2R or, h=R`
`therefore h/d=4/3`