# Fundamentals of Physics Chapter 13 Solutions: Gravitation

Halliday Resnick and Walker Fundamentals of Physics Volume 1 Solutions for Chapter 13 ‘Gravitation’ are crafted carefully to help you understand the chapter for CBSE as well as competitive exams. You must know that gravitational force is the force that holds you to Earth, the Moon in its orbit and the Earth in its orbit around the Sun. Gravitational force is also responsible for holding the galaxies and the entire universe.

Resnick Halliday & Walker Fundamentals of Physics Volume 1 Gravitation Chapter discusses different topics like newton’s law of gravitation, the principle of superposition, gravitation near earth’s surface, gravitation inside the earth, gravitational potential energy, Kepler’s laws, satellites with orbits and energy, einstein and gravitation and the principle of equivalence. It contains 9 modules with an estimate of 101 questions. The questions range from basic to advanced levels that help you to score good marks in competitive exams like JEE, NEET and BITSAT.

Our subject matter experts provide comprehensive solutions for Resnick Halliday and Walker Fundamentals of Physics Volume 1 Gravitation for Class 11 and Class 12 preparation along with JEE Physics. All the solutions are 100% correct and will help you revise all the basics of gravitation that would allow you to solve any questions related to it in the exams. Follow our solutions today and get all your doubts related to this chapter solved quickly.

## Important topics for Resnick Halliday & Walker Fundamentals of Physics Volume 1 Solutions Chapter 13: Gravitation

**The Law of Gravitation**

Any particle in the entire universe easy attracts another particle only with a gravitational force which is measured by:

F = Gm_{1}m_{2}/r^{2} , where m1 and m2 are the particle masses, r is the separation, and G is the gravitational constant. The value of G = 6.67 x 10^{-11} N m^{2}/ kg^{2}.

**Gravitational Behavior of Uniform Spherical Shells**

In order to find the gravitational force between the extended bodies, you will have to add the individual forces that act on the individual particles within the bodies. But if one of the body is a uniform spherical shell, the net gravitational force that it will exert on the other body will be determined as if the entire mass of the body is located at its centre.

**Superposition **

Gravitational force mainly follows the rule of the principle of superposition. Like, if n particles interact, then the net force that acts on the *n *particle is the sum of forces on it from all the other particles at a particular time. In the chapter, you will be able to know how you can find the sum of these forces.

**Gravitational Acceleration**

The gravitational acceleration is only because of a particle that experiences a gravitational force. Whenever a particle is at a distance r from the centre of a uniform spherical shell with mass M, then the magnitude of gravitational force can be found by:

We know that, F= ma_{g},

This gives us,

a_{g}= GM/r^{2}. Here, a_{g} is the gravitational acceleration, and M is the mass of the body.

**Free Fall Acceleration and Weight **

The mass of the earth is not distributed uniformly because the planet is not perfectly spherical. As the earth rotates, the actual free-fall acceleration of a particle near the earth slightly differs from the gravitational acceleration and the particle’s weight differs from the magnitude of gravitational force on it as calculated by Newton’s law of gravitation.

**Gravitation within a Spherical Shell**

In this section, you will get to know how to find the force magnitude when a uniform shell of matter exerts zero gravitational force on a particle located inside it.

**Gravitational Potential Energy**

It is the negative of the work that will be done by the gravitational force of any particle acting on the other if the separation between the particles is changed from infinite to r.

**The Potential Energy of a System**

If there are more than two particles in a system, then the total gravitational potential energy U is the sum of terms representing the potential energies of all the pairs.

**Escape Speed**

An object easily escapes the gravitational pull of an astronomical body that has *M* as mass and *R* as the radius if the speed of the object almost near to the surface of a body is equal to the escape speed. The chapter will tell you how to calculate escape speed.

**Kepler’s Laws**

Kepler’s law has given three laws to see the motion of satellites which are both natural and artificial. The chapter will tell you in detail about the below-listed laws:

- The law of orbits
- The law of areas
- The law of periods

**The energy in Planetary Motion**

This energy is calculated as the sum of kinetic energy and potential energy.

**Einstein’s View of Gravitation**

Einstein says that acceleration and gravitation are equivalent. Under this topic, you will know about the theory of gravitation which explains the gravitational effects in terms of space curvature.

### Exercise-wise Discussion of Halliday Resnick & Walker Fundamentals of Physics Volume 1 Solutions Chapter 13: Gravitation

**Module 1: Newton’s Law of Gravitation**

This module has 5 questions in which you need to find the ratio of masses that increase the gravitational forces, the decrease in weight in the change of position of the Moon, the ratio of forces acting on the two bodies.

**Module 2: Gravitation and Principle of superposition**

Module 2 has 11 questions in which you will find out the magnitude and direction of gravitational force or the coordinates of a 3D figure.

**Module 3: Gravitation Near Earth’s Surface **

This module has 7 questions that cover these two topics. You will have to find the weight of an object on the surface of the moon or another planet, altitude on which the gravitational force be a or b, change in weight while riding an elevator, gravitational acceleration.

**Module 4: Gravitation Inside Earth**

Module 3 has five questions. You will be solving questions on finding the magnitude of net gravitational force, distance, gravitational acceleration.

**Module 5: Gravitational Potential Energy**

With 14 questions in module 5, you will find the gravitational potential energy, the ratio of the mean density of two bodies, change in gravitational potential energy, the work is done, kinetic energy, and speed.

**Module 6: Planets and Satellites: Kepler’s Law**

There are around 17 questions in this module. You will have to solve questions on topics like finding the mass and density of a body, finding gravitational potential energy, the period of revolution, calculating the semimajor axis, the radius of a body, and speed.

**Module 7: Satellites: Orbits and Energy**

This module has 9 questions in which you need to find out the total mechanical energy, identifying which satellite has more energy when compared, calculating the period of revolution, kinetic energy, angular momentum, speed.

**Module 8: Einstein and Gravitation**

This module has only one question in which you need to find the time taken for an object to reach the floor.

**Module 9: Additional Problems**

This module has 31 questions. In these questions, you will have to find the speed, gravitational acceleration, mass of the body, calculating rotation period, angular speed, kinetic energy, semimajor axis, mechanical energy, the amount of work done, and the difference in the weight of two bodies.

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