Question

Calculate the force of gravity on the 0.50-kg mass if it were 6.4×106 m above earth's surface (that is, if it were two earth radii from earth's center).

Answer 1

Radius of Earth is given as

$R = 6.4 * 10^6 m$

now here the height from the surface of earth is same as that of radius

$h = 6.4 * 10^6 m$

now here the acceleration due to gravity at this height is given as

$g' = \frac{GM}{(R+h)^2}$

$g' = \frac{GM}{4R^2}$

$g' = \frac{g}{4}$

now the force of gravity on the given object will be

$F = mg'$

$F = m*\frac{g}{4}$

$F = 0.5 * \frac{9.8}{4}$

$F = 1.225 N$

so the force of gravity on it is 1.225 N