## How to Calculate Work Done By Gravitational Force

In our day-to-day life, we see innumerable instances where gravity works with force. We know that in this universe there is a constant motion and force in the form of pushes and pulls. Among the many motions, there are four significant elementary forces, depending on which all sorts of phenomena are created. They are gravitational force, strong force, weak force and electromagnetic force.

Among all, the gravitational force, coined as Newton’s Universal Law of Gravitation, states that “Everybody in the universe pulls every other body with a force that is directly proportional to their mass-produced and inversely proportional to the square of distance squared between them.”

The Gravitational force formula is given by:

\[ F = G \frac{m_{1}m_{2}}{r^{2}} \]

Where,

G = universal gravitational constant,

m1 and m2 = mass of bodies

r = distance between the two masses

Gravity is basically a force that attracts objects towards the earth - Forces have the ability to work and that inherently means that gravity does the work.

When force is applied to an object, the force performs the work. For example, if you throw a ball, the force applied to the ball makes the ball go farther than you and travels a distance, therefore the work is done. The work will be related to the force applied and the distance is travelled or made depending on it, i.e if you throw the ball with less force, the distance covered by the ball will be smaller, relevant to the force you applied; similarly, if you throw the ball with much force, the distance covered will be lengthy.

Gravitational force is the force that keeps anything with a mass attracted to the earth. If any physical body with mass moves under the gravitational force, it is performed under the work of the gravitational force called gravitational work.

This is the formula.

work = mass* gravity* height

The equation is written

W = m*g*h

We have:

W = work done by gravity

m = mass

g = gravity

h = height

### Solved Questions for Work Done by Gravity

1) Calculate the force of gravitation between the earth and the Sun where the mass of the earth = 6 x 1024 kg and the mass of the Sun = 2 x 1030 kg. The average distance between the two is 1.5 x 1011 m.

Ans. The mass =6 x 1024 kg

The mass of the Sun = 2 x 1030 kg

The average distance between the earth and the Sun, (d) = 1.5 x 1011 m

The gravitational constant (G) = 6.67 x 10-11 Nm2 /Kg2

The gravitational force of attraction between m1 and m2 can be found out using this formula

\[ F = G \frac{m_{1}m_{2}}{r^{2}} \]

\[ F = 6.67 \times 10^{-11} \frac{2\times10^{30} \times 6 \times 10^{24}}{(1.5\times10^{11})^{2}} \]

F = 3.557 × 1022 N.

2) A body of 55 kg falls from the fifth floor of a building 90 m high. What is the work done by gravitational force?

Answer: The body falls within the action of the force of gravity. To calculate the work done, this formula should be used: m = 55 kg, g = 9.8 m/s^{2}, h = 90 m.

W = 55 kg x 9.8 m/s^{2} x 90 m

W = 48,510 J.

Therefore, this is the work done by the gravitational force.

### Conclusion

This is how we can derive and calculate the work done by the gravitational force. Understand how the formula has been derived to use it well in the exercise problems. Practice using this formula and make sure you use the units of these physical quantities aptly.

## FAQs on Work Done by Gravity Formula

**1. What is the gravitational force formula?**

Using the formula of gravitation

**(1). Gravitational force :**

This is a product of the mass of an object divided by the square of the distance.

Mathematically,

\[ F = \frac{GmM}{r^{2}} \]

Where G = gravitational constant

M = mass of one object

m = mass of another object

r = distance between the objects

**(2). Acceleration due to gravity :**

The product of the mass of the object and gravitational constant and divided by the square of the distance.

Mathematically,

\[ g = \frac{GM}{r^{2}} \]

Where G = gravitational constant

M = mass

r = distance

**2. What is gravitational force?**

In general terms, the force between two objects that attract each other is called gravitational force. Gravitational force is the force that keeps anything with a mass attracted to the earth. It is a non-contact force that acts all the time between two objects or bodies.