# Newton’s Law of Universal Gravitation Formula | Problems

Newton’s law of universal gravitation formula states that the gravitational force (FG) between the two objects directly depends upon their masses (m1 and m2) and inversely depends upon the square of distance (r) between them. Here’s the formula of newton’s law of universal gravitation: FG = G [m1 m2] ÷ r2

Let’s solve some problems based on this formula, so you’ll get a clear idea.

## Newton’s Law of Universal Gravitation Practice Problems

Problem 1: Calculate the gravitational force between a 8 kg wooden crate and a 100 kg car. The distance between the centers of a wooden crate and a car is 200 m. (Take the value of universal gravitational constant, G = 6.67 × 10-11 N m2/kg2)

Solution:

Given data:
Gravitational force between a wooden crate and a car, FG = ?
Mass of a wooden crate, m1 = 8 kg
Mass of a car, m2 = 100 kg
Distance between the centers of a wooden crate and a car, r = 200 m
Universal gravitational constant, G = 6.67 × 10-11 N m2/kg2

Using the formula of newton’s law of universal gravitation,
FG = G [m1 m2] ÷ r2
FG = (6.67 × 10-11 × 8 × 100) ÷ (200)2
FG = (6.67 × 10-11 × 8 × 200) ÷ (4 × 104)
FG = (2668 × 10-11) ÷ 104
FG = 26.68 × 10-13 N

Therefore, the gravitational force between a wooden crate and a car is 26.68 × 10-13 N.

Problem 2: Calculate the gravitational force between the two spheres of mass 4 kg and 10 kg which are separated by a distance of 500 m. (Take the value of universal gravitational constant, G = 6.67 × 10-11 N m2/kg2)

Solution:

Given data:
Gravitational force between the two spheres, FG = ?
Mass of the sphere 1, m1 = 4 kg
Mass of the sphere 2, m2 = 10 kg
Distance between the two spheres, r = 500 m
Universal gravitational constant, G = 6.67 × 10-11 N m2/kg2

Using the formula of newton’s law of universal gravitation,
FG = G [m1 m2] ÷ r2
FG = (6.67 × 10-11 × 4 × 10) ÷ (500)2
FG = (6.67 × 10-11 × 4 × 10) ÷ (25 × 104)
FG = (1.06 × 10-11) ÷ 103
FG = 1.06 × 10-14 N

Therefore, the gravitational force between the two spheres is 1.06 × 10-14 N.

Problem 3: A 5000 kg satellite and a 4000 kg satellite are floating in space. If the distance between these two satellites is 2500 m, then calculate the gravitational force acting between them. (Take the value of universal gravitational constant, G = 6.67 × 10-11 N m2/kg2)

Solution:

Given data:
Mass of a satellite 1, m1 = 5000 kg
Mass of a satellite 2, m2 = 4000 kg
Distance between the centers of the two satellites, r = 2500 m
Gravitational force between the two satellites, FG = ?
Universal gravitational constant, G = 6.67 × 10-11 N m2/kg2

Using the formula of newton’s law of universal gravitation,
FG = G [m1 m2] ÷ r2
FG = (6.67 × 10-11 × 5000 × 4000) ÷ (2500)2
FG = (6.67 × 10-11 × 20 × 106) ÷ (625 × 104)
FG = (0.2134 × 10-5) ÷ 104
FG = 0.2134 × 10-9 N
FG = 21.34 × 10-11 N

Therefore, the gravitational force between between the two satellites is 21.34 × 10-11 N.

Problem 4: Two asteroids of different masses m1 = 4 × 1015 kg and m2 = 8 × 1014 kg are floating in space. Calculate the gravitational force acting between them, if they are 1010 m apart from each other. (Take the value of universal gravitational constant, G = 6.67 × 10-11 N m2/kg2)

Solution:

Given data:
Mass of the asteroid 1, m1 = 4 × 1015 kg
Mass of the asteroid 2, m2 = 8 × 1014 kg
Gravitational force between the two asteroids, FG = ?
Distance between the two asteroids, r = 1010 m
Universal gravitational constant, G = 6.67 × 10-11 N m2/kg2

Using the formula of newton’s law of universal gravitation,
FG = G [m1 m2] ÷ r2
FG = (6.67 × 10-11 × 4 × 1015 × 8 × 1014) ÷ (1010)2
FG = (213.44 × 1018) ÷ 1020
FG = 213.44 × 10-2
FG = 2.13 N

Therefore, the gravitational force between the two asteroids is 2.13 N.

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