The force between marbles

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?

1 1 megagram = 1 0 6 10^6 grams 1 1 kilogram = 1 0 3 10^{3} grams 1 1 milligram = 1 0 3 10^{-3} grams 1 1 gram

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1 solution

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 m 1 m 2 r 2 \vec{F}_{g} = G \dfrac{m_{1}m_{2}}{r^{2}}
Since the marbles are identical we can reduce the equation to this:
F g = G m 2 r 2 \vec{F}_{g} = \dfrac{Gm^{2}}{r^{2}}
Just got to do some algebraic manipulations and we arrive to an expression to mass:
m = F g r 2 G m = \sqrt{\dfrac{\vec{F}_{g}r^{2}}{G}}
After plugging in the numbers, we get the answer:
m = 1224.071817 kg m = 1224.071817 \text{ kg}
Since the answers are in grams we have to convert the mass ( m m ) from kilograms to grams. So we proceed to multiply it by 1000 (Since 1 kg = 1 0 3 10^{3} g) and then divide it by 1 0 6 10^{6} and the answer should be close to 1 and there we go, because the answer is 1.2 \approx 1.2 .

Obs: G G stands for the Gravitational Constant whose value is 6.674 1 0 11 N m 2 K g 2 6.674*10^{-11}Nm^{2}Kg^{-2} .

Moderator note:

Simple standard approach.

Oops, the distance between the marbles was supposed to be 1 cm. I have corrected the problem.

Thanks for writing the solution. It is very well explained :)

Pranshu Gaba - 5 years ago

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No problem, I have corrected the answer as well.
Thank you for writing the problem!

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