Question

# At what height, is the value of g half that on the surface of earth? (R = radius of the earth)A.) 0.414RB.) RC.) 2RD.) 3.5R

Hint: In this question, g is referred to as the acceleration of gravity. Its value is $9.8{\text{ }}m/{s^2}$ on Earth. That is to say, the acceleration of gravity on the surface of the earth at sea level is $9.8{\text{ }}m/{s^2}$.

We know, $\dfrac{g}{{g'}} = \dfrac{{{r^2}}}{{{R^2}}}$, where g is gravitational force on earth, g' is gravitational force at a height.

Given g' = $\dfrac{g}{2}$

g’ = $\dfrac{{g{R^2}}}{{{r^2}}} = \dfrac{g}{2}$
$\Rightarrow {{\text{r}}^{\text{2}}}{\text{ = 2}}{{\text{R}}^{\text{2}}}$
$\Rightarrow {\text{r = R}}\sqrt {\text{2}} {\text{ = R + h}}$
$\Rightarrow {\text{h = R (}}\sqrt {\text{2}} {\text{ - 1)}}$
= R (1.414 – 1)
= 0.414R.

Hence the option A is the right answer.