Class 9 & 10 Physics

What Is Gravitational Force?

Q: Does mass change when an object is taken to the Moon?

No. Mass remains the same, while weight changes because the Moon's gravitational acceleration differs from Earth's.

Q: What happens to gravitational force if the distance is doubled?

The gravitational force becomes one-fourth because it is inversely proportional to the square of the distance.

Gravity is a force we experience every day. It keeps us on Earth, brings a thrown ball back down, and helps keep planets and moons in their orbits. In this article, we build the idea of gravitational force from the basics and then apply it to numerical problems.

In simple words: Gravitational force is the force of attraction between any two objects that have mass.

1. What Is Gravitational Force?

Every object having mass attracts every other object having mass. This attraction is called gravitational force.

The Earth attracts you towards its centre, which is why you do not float away from its surface. In the same way, you attract the Earth too. The Earth's mass is so enormous compared with your mass that the Earth's motion due to this attraction is not noticeable.

Everyday example: When you drop a pen from your hand, it moves downward because the Earth pulls the pen towards its centre through gravitational force.

2. Important Definitions

Term	Meaning	SI Unit
Gravitational force	The attractive force acting between any two masses.	newton (N)
Mass	The amount of matter in an object. It remains the same at different places.	kilogram (kg)
Weight	The gravitational force with which a celestial body attracts an object.	newton (N)
Acceleration due to gravity	The acceleration produced in a freely falling object due to gravitational attraction.	m/s²

3. Newton's Law of Universal Gravitation

Newton's law of universal gravitation states that every object in the universe attracts every other object with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

F = G\frac{m_1m_2}{r^2}

Here:

F = gravitational force between the two objects
G = universal gravitational constant
m₁ and m₂ = masses of the two objects
r = distance between the centres of the two objects

The value of the universal gravitational constant is .

Remember: Distance is squared in the formula. If the distance becomes twice, the gravitational force becomes one-fourth.

4. What Happens When Mass or Distance Changes?

Change	Effect on Gravitational Force
One mass becomes 2 times	Force becomes 2 times
Both masses become 2 times	Force becomes 4 times
Distance becomes 2 times	Force becomes 1/4
Distance becomes 3 times	Force becomes 1/9
Distance becomes half	Force becomes 4 times

This inverse-square relationship is one of the most important ideas to remember while solving Class 9 and 10 numerical questions.

5. Gravity and Acceleration Due to Gravity

The gravitational attraction of the Earth gives objects an acceleration towards the Earth's centre. This acceleration is called acceleration due to gravity and is represented by g.

g \approx 9.8\,\mathrm{m/s^2}

Near the Earth's surface, we usually take unless a question gives another value. In many school problems, may be used to make calculations easier.

Weight of an Object

Weight is the gravitational force acting on an object because of a planet or other celestial body.

W = mg

Quantity	Mass	Weight
Meaning	Amount of matter in an object	Gravitational force acting on the object
SI unit	kg	N
Depends on location?	No	Yes
Formula	—

6. Solved Numerical Examples

Numerical 1: Force Between Two Masses

Two objects have masses 5 kg and 10 kg. Their centres are 2 m apart. Find the gravitational force between them. Take .

Given:

m₁ = 5 kg
m₂ = 10 kg
r = 2 m

Formula:

F = G\frac{m_1m_2}{r^2}

Substitution:

F = \frac{6.67\times10^{-11}\times5\times10}{2^2}

F = \frac{6.67\times10^{-11}\times50}{4}

F = 8.3375\times10^{-10}\,\mathrm{N}

Answer: The gravitational force is approximately .

Numerical 2: Finding the Weight of a Student

A student has a mass of 50 kg. Find the student's weight on Earth. Take .

Given: m = 50 kg and g = 9.8 m/s²

Formula:

W = mg

W = 50\times9.8

W = 490\,\mathrm{N}

Answer: The student's weight is 490 N.

Numerical 3: Effect of Doubling the Distance

The distance between two masses is doubled while their masses remain unchanged. What happens to the gravitational force?

We know:

F \propto \frac{1}{r^2}

If the new distance is 2r, then:

F' = \frac{F}{2^2}

F' = \frac{F}{4}

Answer: The new gravitational force becomes one-fourth of the original force.

Numerical 4: Finding g from Weight

An object of mass 20 kg has a weight of 196 N on a planet. Find the acceleration due to gravity on that planet.

Given: W = 196 N and m = 20 kg

Using :

g = \frac{W}{m}

g = \frac{196}{20}

g = 9.8\,\mathrm{m/s^2}

Answer: The acceleration due to gravity is 9.8 m/s².

7. Important Formulas at a Glance

Concept	Formula	Use
Universal gravitation		Force between two masses
Weight		Weight of an object near a planet
Acceleration due to gravity		Free-fall calculations near Earth
Distance effect		Questions involving change in distance
Mass effect		Questions involving change in masses

8. Common Mistakes Students Make

Using mass in grams instead of converting it to kilograms.
Forgetting that the distance in Newton's gravitation formula is squared.
Confusing mass in kg with weight in newtons.
Writing the unit of gravitational force as kg instead of N.
Using the value of g without checking whether the question gives a different value.
Using the distance between surfaces when the question requires the distance between the centres of the masses.

9. Quick Revision

Gravitational force: Attractive force between any two masses.

Newton's law: .

Universal constant: .

Acceleration due to gravity: near Earth's surface.

Weight: .

Key idea: More mass means more gravitational force; greater distance means less gravitational force.

10. Frequently Asked Questions

What is gravitational force?

Gravitational force is the attractive force that acts between any two objects having mass.

Is gravitational force always attractive?

In the Class 9 and 10 treatment of gravitation, gravitational force is described as an attractive force.

What is the value of G?

The universal gravitational constant is approximately 6.67 × 10⁻¹¹ N m²/kg².

What is the difference between G and g?

G is the universal gravitational constant, while g is acceleration due to gravity and depends on the celestial body and location.

Why does an object fall towards Earth?

The Earth attracts the object through gravitational force. The resulting acceleration towards the Earth's centre makes the object fall.

Does mass change when an object is taken to the Moon?

No. The mass remains the same. The weight changes because the Moon's gravitational acceleration is different from Earth's.

What happens to gravitational force if the distance is doubled?

The force becomes one-fourth because gravitational force is inversely proportional to the square of the distance.

What is the SI unit of weight?

The SI unit of weight is newton (N), because weight is a force.

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