**This Physics Tutorial will focus on GRAVITATIONAL FIELD. This topic has been explained to ensure you understand it very well. At the end of the tutorial, you can download it for FREE. Please share this page with your friends who may need it.**

This tutorial will explain the Gravitation Field to you like you’ve never seen before.

It’ll explain Newton’s law of universal gravitation.

Then you’ll learn conservative and non-conservative fields.

You’ll then learn acceleration due to gravity.

After the lesson, we will also give you some objective questions to test your knowledge. We strongly recommend that you try it out.

Without much ado, let’s proceed.

Page Contents

## What Is Gravitational Field

In physics, a gravitational field is a field that describes the force exerted on a mass by another mass due to gravity.

Gravity is the force of attraction between two masses, and the gravitational field is a way of quantifying this force at any point in space surrounding a mass.

Didn’t grab that?

Alright, let’s imagine you have a magical friend who loves to pull things towards them but only if those things are close enough. This magical friend creates an invisible force that reaches out from them in all directions. If you have a toy nearby, it will feel a little pull toward your magical friend.

Now, let’s pretend this magical friend is really, really big, like a planet. The invisible force they create is what we call a gravitational field. It’s like an invisible hug that goes all around them. If you have a ball far away from your magical friend, it might not feel the hug as much, but if you bring it closer, the hug gets stronger.

This gravitational field is why things fall down on Earth. Earth is like a giant magical friend, and its gravitational field pulls everything toward it. The bigger and heavier something is, the stronger the hug it feels from the Earth.

So, in simple terms, a gravitational field is like an invisible hug that a big object, like a planet, gives to things around it, making them come closer if they’re not too far away.

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**Newton’s Law of Universal Gravitation**

The concept of a gravitational field was introduced by Sir Isaac Newton in his law of universal gravitation.

According to Newton’s law, every point mass attracts every other point mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

The formula for the gravitational force (F) between two masses (m_{1} and m_{2}) separated by a distance (r) is given by:

F = G ⋅ m_{1}m_{2} / r^{2}

Where:

*F*is the gravitational force,*G*is the gravitational constant,*m*_{1}and*m*_{2} are the masses of the two objects,*r*is the separation between the centers of the masses.

The gravitational field (*g*) at a point in space is defined as the gravitational force per unit mass experienced by a test mass at that point. Mathematically, it is given by:

*g *= *mF*

Where:

*g*is the gravitational field,*F*is the gravitational force,*m*is the test mass.

## Conservative and Non-Conservative Field

In physics, fields can be categorized as either conservative or non-conservative based on certain properties related to energy.

A conservative field is a vector field in which the work done by a force along any path between two points is independent of the path taken. The work done in moving an object from one point to another depends only on the initial and final positions, not on the path taken.

A non-conservative field is a vector field in which the work done by a force in moving an object from one point to another depends on the path taken. The work done is not solely determined by the initial and final positions.

Didn’t get that?

Imagine you have a treasure map, and you want to find the treasure. Now, let’s think about two types of paths you can take:

**Conservative Path:**- If you follow a conservative path, it means that no matter how you get there, the amount of effort you put into walking is the only thing that matters.
- Picture it like climbing a hill. If you climb up and then down, you end up at the same height. The total effort you spent depends only on how high you climbed, not the exact path you took.
- In physics, a conservative field is like this. It doesn’t care about the exact path you take; it only cares about the starting and ending points.

**Non-conservative Path:**- Now, imagine a different path where the landscape is bumpy, and you might have to climb some hills, go down into valleys, and maybe even do some jumping.
- The total effort you put into walking now depends on every little detail of your journey—the bumps, the jumps, and everything in between.
- In physics, a non-conservative field is like this. It cares about the specific path you take. Work done in a non-conservative field depends on the actual journey, not just the starting and ending points.

So, in a nutshell:

**Conservative field:**The total work or effort only depends on the starting and ending points, not on how you got there.**Non-conservative field:**The total work or effort depends on every little detail of the path you took.

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## Acceleration Due to Gravity

Acceleration due to gravity refers to the acceleration experienced by an object in a gravitational field.

Now imagine you have a magic pencil, and you toss it up into the air. What happens? It goes up for a bit, but then it starts to slow down and eventually falls back down, right?

Acceleration due to gravity is like the reason the pencil comes back down. It’s like an invisible force that pulls everything towards the Earth. So, when you throw something up, gravity slows it down until it stops and then pulls it back down.

Here’s the cool part: no matter if you throw a ball, drop a feather, or let go of a helium balloon, gravity is always there, making things fall. Everything on Earth gets this little push from gravity, and that’s why we call it the acceleration due to gravity.

On the surface of the Earth, the acceleration due to gravity is denoted by the symbol *g* and is approximately 9.8m/s^{2} directed towards the center of the Earth. This means that every second, the velocity of an object in free fall will increase by 9.8 m/s9.8m/s downward.

Key points about acceleration due to gravity:

**Magnitude:**The acceleration due to gravity (*g*) is a measure of how much the velocity of an object changes per unit time under the influence of gravity. Near the surface of the Earth,*g*is approximately 9.8m/s^{2}.**Direction:**The acceleration due to gravity is always directed towards the center of the massive object causing the gravitational field, which is usually the center of the Earth. This direction is conventionally considered negative when dealing with vertical motion.**Independence of Mass:**One of the fundamental principles of gravity, as described by Newton’s law of universal gravitation, is that the acceleration due to gravity is independent of the mass of the object. All objects near the Earth’s surface experience the same acceleration due to gravity, regardless of their mass.**Free Fall:**In the absence of air resistance, all objects near the surface of the Earth fall with the same acceleration. This phenomenon is known as free fall. The motion of an object in free fall can be described using the equations of motion under constant acceleration.

The formula for the acceleration due to gravity is given by:

*g*=*m/F*

Where:

*g*is the acceleration due to gravity,*F*is the gravitational force acting on the object,*m*is the mass of the object.

That’s all we will cover in this tutorial.

Now it’s time to know if you actually understood everything that was taught.

Attempt these practice questions to find out.

## Practice Questions

**1:** What is the direction of the gravitational field at a point in space directly above the center of a massive object?

A) Upward

B) Downward

C) Radial outward

D) There is no gravitational field at this point

**2:** In a conservative field, the work done by a force depends on the specific path taken between two points.

A) True

B) False

**3:** If the separation between two masses is halved, what happens to the gravitational force between them according to Newton’s Law of Universal Gravitation?

A) It is halved

B) It is doubled

C) It is quadrupled

D) It remains the same

**4:** The gravitational field strength (*g*) at a point in space is dependent on the mass of the object experiencing the field.

A) True

B) False

**5:** What is the relationship between the gravitational force (*F*) and the mass (*m*) of an object in a conservative gravitational field?

A) *F*∝*m*

B) *F* ∝ *1/m*

C) *F* ∝ *m*^{2}

D) *F* ∝* 1/m*^{2}

**6:** Acceleration due to gravity (*g*) is the same for all objects regardless of their mass.

A) True

B) False

**7:** Which of the following fields is typically non-conservative?

A) Gravitational field

B) Magnetic field

C) Electric field

D) Conservative field

**8:** In a conservative field, the curl of the vector field is always zero.

A) True

B) False

**9:** If an object is taken from the surface of the Earth to a higher altitude, what happens to its weight?

A) It increases

B) It decreases

C) It remains the same

D) It becomes zero

**10:** The acceleration due to gravity on the surface of Mars is greater than the acceleration due to gravity on the surface of the Moon.

A) True

B) False

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**Answers and Explanations**

**Answer: B) Downward**Explanation: The gravitational field is directed towards the center of the massive object, so directly above the center, the field points downward.**Answer: B) False**Explanation: In a conservative field, the work done by a force is independent of the path taken. It depends only on the initial and final positions.**Answer: B) It is doubled**Explanation: According to Newton’s Law of Universal Gravitation, the force is inversely proportional to the square of the separation. Halving the separation doubles the force.**Answer: B) False**Explanation: The gravitational field strength (*g*) is independent of the mass of the object experiencing the field. All objects near the Earth’s surface experience the same*g*.**Answer: A)**Explanation: In a gravitational field, the force (*F*∝*m**F*) is directly proportional to the mass (*m*) of the object.**Answer: A) True**Explanation: Acceleration due to gravity is the same for all objects regardless of their mass. It is approximately 9.8 m/s29.8m/s2 on the surface of the Earth.**Answer: C) Electric field**Explanation: Electric fields are often non-conservative, especially in the presence of resistive elements.**Answer: A) True**Explanation: In a conservative field, the curl of the vector field is always zero. This is a consequence of the path-independence of the work done.**Answer: B) It decreases**Explanation: As you move to a higher altitude, the distance from the center of the Earth increases, and the gravitational force (and weight) decreases.**Answer: B) False**Explanation: The acceleration due to gravity depends on the mass of the celestial body. On Mars, the gravitational acceleration is weaker than on Earth, and on the Moon, it is even weaker than on Mars.

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