Question

The height at which the acceleration due to gravity becomes `g/4` in terms of R is ______.

[R = the radius of the earth]

Options

• `R/sqrt 2`

• R

• `sqrt 2 R`

• 2 R

Answer 1

The height at which the acceleration due to gravity becomes `g/4` in terms of R is R.

Explanation:

Given: `(g')/g = 1/4`

`1/4 = (R^2)/((R + h)^2)`

⇒ `R^2/(R + h) = 1/sqrt 4`

∴ `sqrt n R` = R + h

∴ `R (sqrt n - 1)` = h

R(2 − 1) = R = h