Question

How many times greater is the force of gravity on a 6.0 kg object lying on the surface of a moon than on a 6.0 kg object orbiting at a distance 6 times greater than the radius of the moon?

Answer 1

if an object is on the surface of Moon then the force of gravitation is given as

$F_1 = \frac{GM(6kg)}{R^2}$

here

M = mass of moon

R = radius of moon

now in other case we have the same object orbiting at distance 6 times greater than the radius of moon

so the force of gravitation is given as

$F_2 = \frac{GM(6kg)}{(6R)^2}$

now we will find the ratio of two forces

$\frac{F_1}{F_2} = \frac{1}{1/36} = 36$

so here the force of gravity on orbiting object is 36 times less than the object which is placed on the surface of moon