Suppose the mass of each of two spherical objects is doubled, and the distance between their centers is three times as large. How is the magnitude of the force of gravity between them affected?
It is 2/3 as large.

Question

Suppose the mass of each of two spherical objects is doubled, and the distance between their centers is three times as large. How is the magnitude of the force of gravity between them affected?
It is 2/3 as large.

anonymous · Answer

It is 4/3 as large.

 It is 4/9 as large.

 It is 3/2 as large.

It is 2/9 as large.

It is 2/3 as large.

whpalmer4 · Answer

$$F_1 = \frac{Gm_1m_2}{r^2}$$ If we use new masses and radius where new mass = 2* old mass, and radius = 3* old radius, we get 
$$F_2 = \frac{G(2m_1)(2m_2)}{(3r)^2} = \frac{4}{9}\frac{Gm_1m_2}{r^2} = \frac{4}{9}F_1$$
So it is 4/9 as large.  Gravity follows the inverse square law so tripling the distance cuts the force to 1/9, and doubling the two masses increases it by only a factor of 4, which doesn't offset the loss due to increased distance.

whpalmer4 · Answer

If we tripled the mass of each object, then the attraction would be constant.