# Practical Exercise 4: Gravitational Force

**Practical Exercise**: Calculate the magnitude of the gravitational force between two grains, which are perfect spheres with a radius of 0.1 m and a density of 1,300 kg m^{–3}, located at a distance of 1 m from each other.

Answer: The gravitational force is calculated using the equation ,

where *G = 6,67 ∙ 10 ^{−11} m^{3} · kg^{−1} · s^{−2}.* First, we have to calculate the weight of the grains. It is a sphere whose volume is calculated according to the equation .

he result after substitution *V = 4,2 ∙ 10 ^{−3} m^{3}.* The weight is calculated

*m = ρ V*. The grain weight is 5,5 kg.

The gravitational force is then *Fg = 2,0 ∙ 10 ^{−9} N*.

**Practical Exercise**: Now, imagine that one grain is 10 meters in size and the grains are 1,000 meters apart. Calculate the magnitude of the gravitational force between the grains.

**Answer: ***V = 4,2 ∙ 10 ^{3} m^{3} , m = 5,5 ∙ 10^{6} kg, Fg = 2,0 ∙ 10^{−3} N*.

**Practical Exercise:** What would be the magnitude of the gravitational force if one grain had a diameter of 10 km, the other 0.1 meters and they were 15 km apart?

**Answer:** *V _{1} = 4,2 ∙ 10^{12} m^{3} , m^{1} = 5,5 ∙ 10^{15} kg, V_{2} = 4,2 ∙ 10^{−3} m^{3} , m^{2} = 5,5 kg*,

*Fg = 9,0 ∙ 10 ^{−3} N.*