Question

At what height h above earth, the value of g becomes `g/2` (where R = radius of earth)?

Options

• `(sqrt2-1)"R"`

• `sqrt2  "R"`

• `(sqrt2+1)"R"`

• `"R"/sqrt2`

Answer 1

`(sqrt2-1)"R"`

Explanation:

`"g'" = "g" ("R"/"R+h")^2`

`"Given  g'" = "g"/2`

`1/2 = ("R"/"R+h")^2 Rightarrow 1/sqrt2 = "R"/"R+h"`

`Rightarrow "h" = "R" (sqrt2 - 1)`