Two identical marbles are kept 1 cm apart.
If the gravitational force between the marbles is 1 N, what is the approximate mass of the marbles?
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Relevant wiki: Gravity
Well this is a really easy question, I don't understand why it is on Level 3, but ok, here it goes the answer.
F g = G r 2 m 1 m 2
Since the marbles are identical we can reduce the equation to this:
F g = r 2 G m 2
Just got to do some algebraic manipulations and we arrive to an expression to mass:
m = G F g r 2
After plugging in the numbers, we get the answer:
m = 1 2 2 4 . 0 7 1 8 1 7 kg
Since the answers are in grams we have to convert the mass ( m ) from kilograms to grams. So we proceed to multiply it by 1000 (Since 1 kg = 1 0 3 g) and then divide it by 1 0 6 and the answer should be close to 1 and there we go, because the answer is ≈ 1 . 2 .
Obs: G stands for the Gravitational Constant whose value is 6 . 6 7 4 ∗ 1 0 − 1 1 N m 2 K g − 2 .