Edited By Team Careers360 | Updated on Sep 26, 2024 10:34 AM IST

Have you ever wondered how you can walk on the ground freely? or when a fruit falls from a tree or something drops from a height, it always heads for the ground? This is exactly what Sir Isaac Newton wondered and offered the world the concept of gravitation. In simple words, Gravitation is the force operating between two objects on the earth. So any thrown object will be attracted toward the earth and will fall on earth. The gravitational force has a very important role which allows us to live in this wonderful world. If gravity disappeared suddenly then we would all start to float immediately. So it is very important to study Gravitational.

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Gravitational force is an attractive force acting between two masses $m_1$ and $m_2$ separated by a distance $r$.

Directly proportional to the product of their masses, i.e., $F \approx\left(m_1 m_2\right) \ldots$ (1)

Inversely proportional to the square of the distance between their centre, i.e., $\left(F=1 / r^2\right) \ldots$. (2)

On combining equations (1) and (2), we get,

\begin{aligned}

& F \propto \frac{m_1 m_2}{r^2} \ldots(1) \\

& F=G \times \frac{m_1 m_2}{r^2} \ldots (2)

\end{aligned}

Then the Gravitational force $F=\frac{G m_1 m_2}{r^2}$

After studying that Gravitation force operates between any two objects on the earth, You may wonder and ask why not all bodies attract each other and stick together due to gravitational force. So answer to this question is that Gravitational Force is the weakest among all the four fundamental forces known to us now.

Let's Suppose 2 similar balls of mass 1 kg are placed 1m apart then the gravitational force acting between them is simply G which is equal to $6.6710 * 10^{-11} \mathrm{Nm}^2(\mathrm{~kg})^{-2}$ As you see this is a very negligible attractive force.

The vector form of Newton's law of gravitation signifies that the gravitational forces acting between the two particles form an action-reaction pair.

From the above figure, it can be seen that the two particles of masses are placed at a distance.

$

\overrightarrow{r_{21}}=\left(\overrightarrow{r_2}-\overrightarrow{r_1}\right)

$

The direction of the vector is from $m_1$ to $m_2$

Therefore, the force applied on $\mathrm{m}_2$ by $\mathrm{m}_1$ is

$

\overrightarrow{F_{21}}=-\frac{G m_1 m_2}{r_{21}^2} r_{21}

$

The negative sign indicates the attractive nature of the force.

Similarly, force on $\mathrm{m}_1$ and $\mathrm{m}_2$

$

\vec{F}_{12}=-\frac{G m_1 m_2}{r_{12}^2} r_{\hat{12}}

$

Since,

$

\hat{r_{12}}=-\hat{r_{21}}

$

$

\vec{F}_{12}=-\frac{G m_1 m_2}{\left(-r_{21}\right)^2}\left[-\hat{r}_{21}\right]

$

$

\begin{aligned}

& \vec{F}_{12}=\frac{G m_1 m_2}{\left(r_{21}\right)^2}\left[r_{21}\right] \\

& =-\overrightarrow{F_{21}}

\end{aligned}

$

Hence, the applied forces are equal and opposite. Also, the gravitational force follows Newton's third law.

**Let's have a look at how g value changes due to the shape of the earth**

$R_e \rightarrow$ Radius of equator

$R_p \rightarrow$ Radius of pole

$

R_{\text {equator }}>R_{\text {pole }}

$

The Equatorial radius is about 21 km longer than the polar radius.

So $g_{\text {pole }}>g_{\text {equator }}$

In fact

$

g_p=g_e+0.018 \mathrm{~m} / \mathrm{s}^2

$

Or we can say that Weight increases as the body is taken from equator to pole.** **

You will also learn about satellites and their motion in space. You will also learn to calculate their orbital velocity, their escape velocity, etc.** **

**Related topics,**

According to Sir Isaac Newton, gravity is that force which pulls two masses. The law of gravitation as given by Newton states that: this force is directly proportional to the product of mass and inversely proportional to distance squared. Gravitation is weak but universal; it affects all objects in the universe equally regardless of their size or composition. This force obeys Newton’s third law of motion, i.e., for every action, there is an equal but opposite reaction; it also varies with different shapes of the earth such that it is stronger at the poles than at the equator.

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1. What is Newton’s Law of Gravitation?

Newton's Law of Gravitation states that every mass attracts every other mass with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.

2. Why don't we feel the gravitational pull between smaller objects around us?

The gravitational force between small objects is extremely weak due to their small masses, so it's negligible compared to Earth's gravitational pull.

3. How does gravity vary with altitude?

Gravity decreases with increasing altitude as the distance from Earth's centre increases. The farther you are from the Earth's surface, the weaker the gravitational pull.

4. What is the value of the gravitational constant (G)?

The gravitational constant (G) is approximately $6.674 \times 10^{-11} \mathrm{Nm}^2 / \mathrm{kg}^2$. It is a fundamental constant used in the equation for gravitational force.

5. Why does Earth exert a gravitational pull on all objects?

Earth has a large mass, and according to Newton's law, all masses attract each other. The Earth's gravitational pull is strong enough to keep everything grounded and gives objects weight.

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Weightlessness

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Gravitation - Notes, Topics, Formulas, Books, FAQs

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Mass And Density Of Earth

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Work Done Against Gravity

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Escape Velocity

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Acceleration Due To Gravity

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Get answers from students and experts

**Correct Answer: ** It is the force causing tides due to the stars and the earth

**Solution : ** The correct option is **It is the force causing tides due to the stars and the Earth.**

The universal law of gravitation primarily describes the gravitational attraction between two masses, such as the Earth and an object on or near its surface. Tides are caused by the gravitational forces exerted by the Moon and the Sun on Earth's oceans, not stars. While stars do exert gravitational forces, their effects on Earth's tides are negligible compared to the Moon and the Sun.

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