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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?

Respuesta :

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

[tex]W_{moon} = \frac{1}{6}W_{earth}[/tex]

[tex]W_{moon} = \frac{1}{6}(100)[/tex]

[tex]W_{moon} = 16.7 N[/tex]

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

[tex]\frac{GM}{r^2} = \frac{GM}{6R^2}[/tex]

[tex]r^2 = 6R^2[/tex]

[tex]r = 2.45 R[/tex]

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