Question

What is the value of acceleration due to gravity at height equal to half the radius of earth from surface of earth. [take $g=10m/s^2$ at earth surface]

Answer 1

Let the radius of earth from surface of earth is $R$ and the height equal to half the radius of earth from surface of earth is $h$.

The acceleration on the surface of earth due to gravity is given as,

$g=\frac{GM}{R^2}$

The acceleration at a height due to gravity is given as,

$g^{\prime }=\frac{GM}{h^2}$

$=\frac{GM}{{\left(\frac{R}{2}\right)}^2}$

$=4g$

$=4\times 10$

$=40m/s^2$

Thus, the value of acceleration at a height due to gravity is $40m/s^2$.