Question

What will an object weigh on the Moon's surface if it weighs 100 N on Earth's surface? (b) How many Earth radii must this same object be from the center of Earth if it is to weigh the same as it does on the Moon?

Answer 1

Answer:

Part a)

W = 16.7 N

Part b)

r = 2.45 R

Explanation:

Part a)

As we know that acceleration due to gravity on the surface of moon is 1/6 times the gravity on the surface of earth

So the force due to gravity will decrease by the factor of 6

so we will have

$W_{moon} = \frac{1}{6}W_{earth}$

$W_{moon} = \frac{1}{6}(100)$

$W_{moon} = 16.7 N$

Part b)

For the same value of the weight as the surface of moon the acceleration due to gravity of earth must be 1/6 times

so we have

$\frac{GM}{r^2} = \frac{GM}{6R^2}$

$r^2 = 6R^2$

$r = 2.45 R$