**Newton’s law of universal gravitation formula** states that the **gravitational force** (F_{G}) between the two objects directly depends upon their **masses** (m_{1} and m_{2}) and inversely depends upon the square of **distance** (r) between them. Here’s the formula of newton’s law of universal gravitation: **F**_{G}** = G [m**_{1}** m**_{2}**] ÷ r**^{2}

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 m^{2}/kg^{2})

Solution:

Given data:

Gravitational force between a wooden crate and a car, F_{G} = ?

Mass of a wooden crate, m_{1} = 8 kg

Mass of a car, m_{2} = 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 m^{2}/kg^{2}

Using the formula of newton’s law of universal gravitation,

F_{G} = G [m_{1} m_{2}] ÷ r^{2}

F_{G} = (6.67 × 10^{-11} × 8 × 100) ÷ (200)^{2}

F_{G} = (6.67 × 10^{-11} × 8 × 200) ÷ (4 × 10^{4})

F_{G} = (2668 × 10^{-11}) ÷ 10^{4}

F_{G} = 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 m^{2}/kg^{2})

Solution:

Given data:

Gravitational force between the two spheres, F_{G} = ?

Mass of the sphere 1, m_{1} = 4 kg

Mass of the sphere 2, m_{2} = 10 kg

Distance between the two spheres, r = 500 m

Universal gravitational constant, G = 6.67 × 10^{-11} N m^{2}/kg^{2}

Using the formula of newton’s law of universal gravitation,

F_{G} = G [m_{1} m_{2}] ÷ r^{2}

F_{G} = (6.67 × 10^{-11} × 4 × 10) ÷ (500)^{2}

F_{G} = (6.67 × 10^{-11} × 4 × 10) ÷ (25 × 10^{4})

F_{G} = (1.06 × 10^{-11}) ÷ 10^{3}

F_{G} = 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 m^{2}/kg^{2})

Solution:

Given data:

Mass of a satellite 1, m_{1} = 5000 kg

Mass of a satellite 2, m_{2} = 4000 kg

Distance between the centers of the two satellites, r = 2500 m

Gravitational force between the two satellites, F_{G} = ?

Universal gravitational constant, G = 6.67 × 10^{-11} N m^{2}/kg^{2}

Using the formula of newton’s law of universal gravitation,

F_{G} = G [m_{1} m_{2}] ÷ r^{2}

F_{G} = (6.67 × 10^{-11} × 5000 × 4000) ÷ (2500)^{2}

F_{G} = (6.67 × 10^{-11} × 20 × 10^{6}) ÷ (625 × 10^{4})

F_{G} = (0.2134 × 10^{-5}) ÷ 10^{4}

F_{G} = 0.2134 × 10^{-9} N

F_{G} = 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 m_{1} = 4 × 10^{15} kg and m_{2} = 8 × 10^{14} kg are floating in space. Calculate the gravitational force acting between them, if they are 10^{10} m apart from each other. (Take the value of universal gravitational constant, G = 6.67 × 10^{-11} N m^{2}/kg^{2})

Solution:

Given data:

Mass of the asteroid 1, m_{1} = 4 × 10^{15} kg

Mass of the asteroid 2, m_{2} = 8 × 10^{14} kg

Gravitational force between the two asteroids, F_{G} = ?

Distance between the two asteroids, r = 10^{10} m

Universal gravitational constant, G = 6.67 × 10^{-11} N m^{2}/kg^{2}

Using the formula of newton’s law of universal gravitation,

F_{G} = G [m_{1} m_{2}] ÷ r^{2}

F_{G} = (6.67 × 10^{-11} × 4 × 10^{15} × 8 × 10^{14}) ÷ (10^{10})^{2}

F_{G} = (213.44 × 10^{18}) ÷ 10^{20}

F_{G} = 213.44 × 10^{-2}

F_{G} = 2.13 N

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

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