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# Gravitational force net

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A 21.0 kg sphere is at the origin and a 5.00 kg sphere is at (x,y) = (20cm,0cm). At what point can you place a small mass, such that the net gravitational force on it, due to the sphere's is zero?

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The gravitational force between two masses is given by:
(1.1)
Where G is the gravitational constant and r is the distance between the masses.
Let M be between M1 (distance ) and mass M2 (distance )
For the mass M to be at rest, the magnitude gravitational pull applied by M1 must be equal to the magnitude of the gravitational pull applied by M2:
(1.2)
If the distance between M1 and M2 is R then
(1.3)
Plugging this in (1.2) we get:

(1.4)
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(1.5)
If we set then since we cannot have the correct solution is:
(1.6)
In our case, let M1 be the heavier mass at the origin, then:

The mass must be positioned at a distance from the origin along the x axis.

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