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

Answer

C

Explanation

As `(gR^(2))/(R+h)^(2)=g(1-(h)/(R ))`
`rarr (1-(h)/(R ))(1+(h^(2))/(R^(2))+(2h)/(R ))=1`
`rarr (h)/( R)((h^(2))/(h^(2))+(h)/(R )-1)=0`
`rarr h=(sqrt(5)R-R)/(2)`