# Two balls, each with a mass of 0.879 kg, exert a gravitational force of 8.04 × 10^−11 N on each other. How far apart are the balls? The value of the universal gravitational constant is 6.673 × 10^−11 N m^2/kg^2 . Answer in units of m.

## Expert Answers According to the Universal Law of Gravitation, any two bodies exert a gravitational force on each other and this force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Mathematically,

`F = (Gm_1m_2)/(r^2)`

where, F is the gravitational force, G is the universal gravitational constant, m1 and m2 are the masses of the objects and r is the distance between them.

In the given case, m1 = m2 = 0.879 kg; F = `8.04 xx 10^(-11)`  N and

G = `6.673 xx 10^(-11) Nm^2 /(kg)^2`

Substituting the value of these variables into the equation, we get,

`r^2 = Gm_1m_2/F`

`r^2 = (6.673 xx 10^(-11) xx 0.879 xx 0.879)/(8.04 xx 10^(-11))`

Solving this equation, we get, r = 0.8 m

that is, the two balls are 0.8 m away from each other.

Hope this helps.

Approved by eNotes Editorial Team

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