At what height, the weight of the body is same as that at same depth from the earth's surface (take, earth's radius = R)

Options

A. `(sqrt(3) R - R)/2 `
B. `(sqrt(5))/2 R-R `
C. ` (sqrt(5) R-R)/2`
D. `R/2`

Answer

C

Explanation

` (g_(0))/((1+h/R)^(2) ) = g_(0)(1- h/R)`
` (R^(2))/((R+h)^(2)) = ((R-h))/R `
`R^(3) = (R-h) (R+h)^(2)`
` R^(3) = (R-h) (R^(2) +2h +h^(2))`
on solving we get,
`h = (sqrt(5)R-R)/2 `