Imagine Earth to be a solid sphere. If the value of acceleration due to gravity at a depth 'd' below Earth's surface is the same as its value at a height 'h' above its surface and is equal to `g/4` then the ratio of `h/d` will be ......

Options

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

Answer

B

Explanation

`implies g(h) =g/(1+(h)/R)^2`
`:.g/4=g/(1+(h)/R)^2`
`:. 4=(1+(h)/R)^2`

`:. 2 = 1+h/R`
`:.h/R =1 " "...(1)`
`implies g(d) = g(1-d/R)^2`
`:.g/4=g (1-d/R)`
`:. 1/4 = 1 - d/R`
`:. d/R = 1-1/4`
`:. d/R =3/4 " "...(2)`
`:. ` Taking ratio of equ . (1) and (2)
`h/d =4/3`