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Two objects attract each other gravitationally with a force of 3.0×10−10N when they are 0.45m apart. Their total mass is 4.0kg . find the individual masses

Sagot :

AL2006
If everything is in meters and kilograms, then the gravitational force
between 2 masses is

F = G M₁ M₂ / R²

G = 6.67 x 10⁻¹¹
M₁ and M₂ =  the masses of the two masses
R = the distance between their centers.

When we plug in 3 x 10⁻¹⁰ for the force, and 0.45 for the distance,
we get the product of the 2 objects  M₁M₂ = about 0.911 , and
that's as far as we can go without some more information.

The question says that the two masses add up to 4.0 kg.
So now we know that M₁M₂ = about 0.911 and (M₁ + M₂) = 4.0 kg.
With this, we immediately step into a big squishy quadratic equation,
whose solutions are:

one mass = 3.758 kg
the other mass = 0.242 kg .
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