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Gravity IIT JEE Study Material

The natural phenomenon by which all the objects with mass are brought towards one another, including objects like atoms, photons, stars, planets, etc., is called gravity or acceleration due to gravity. Its S.I. unit is m s -2.

The Universal Law of Gravitation

When one day Newton watched an apple fall from a tree, he wondered what invisible forces drove the apple to fall down.

Science has described gravity as a certain attractive force exerted by all the objects in the universe. According to the universal law of gravitation, every single object in the universe attracts every other object with force directed along the line of centres for the two objects that is proportional to the product of their masses and inversely proportional to the square of the separation between the two objects.

Fย โˆ m1m2/d2

F = G (m1m2/d2ย )

Here, m1 and m2 are the masses of the two particles.

d is the distance between the two masses.

G is the gravitational constant = 6.673 x 10-11 Nm2kg-2

The law of gravitation led to the explanation of Kepler’s laws and terrestrial gravitation.

Gravity exists everywhere. But the Moon does not have a strong gravity as the Earth. One might wonder if this force of gravity is all prevalent, then why don’t the chairs and tables jump at each other?

This is because the force of gravity of the Earth is much stronger than the chair and table’s force of gravity. It also depends on how far away you are from this force of gravity. The farther away you go from the Earth, the less the force of gravity affects you.

Gravitational Potential Energy

The energy possessed by an object because of its position in the gravitational field is called gravitational potential energy. The equation of gravitational potential energy can be calculated from the law of gravity, and it is equal to the amount of work done against gravity to bring the mass to the given point in space. The gravitational force is inversely proportional to the square of the distance; therefore, the force will be zero for a large distance. So, the gravitational potential energy will be negative near a planet since gravity does positive work as the mass approaches.ย  The expression for gravitational potential energy associated with two particles separated by a distance r is given as

U = – Gm1m2/r

This expression is most useful for calculating the escape velocity.

The Gravitational Potential Energy of a System

Change in the gravitational potential energy U (r) of two point masses, m1 and m2, as their separation is changed from r1to r2 is given by,

\(\begin{array}{l}\mathbf{U\left ( r_{2} \right )\;-\;U\left ( r_{1} \right )\;=\;\frac{G\;m_{1}\;m_{2}}{r_{1}\;-\;r_{2}}}\end{array} \)

At infinite separation, the gravitational potential energy (Ur) is assumed to be 0.

i.e.,

\(\begin{array}{l}\mathbf{U\left ( r \right )\;=\;-\;\frac{G\;m_{1}\;m_{2}}{r}}\end{array} \)

Gravitational Potential (V)

The gravitational potential at any point is the amount of work done per unit of mass that is required to move an object to that point. The gravitational potential at any point is the gravitational potential energy per unit mass.

V = U/m

U is the gravitational potential energy.

m is the mass of the object.

The mathematical expression for the potential is given by

\(\begin{array}{l}V(x)=\frac{W}{m}=\frac{1}{m}\int_{\infty }^{x}F.dx\end{array} \)
\(\begin{array}{l}=\frac{1}{m}\int_{\infty }^{x}\frac{GmM}{x^{2}}.dx = -\frac{GM}{x}\end{array} \)

Gravitational Potential (V) Due to Uniform Solid Sphere

A. At distance r from the centre (Outside the sphere)

\(\begin{array}{l}\mathbf{V\;=\;-\;\frac{GM}{r}}\end{array} \)

B. At distance r from the centre (Inside the sphere)

\(\begin{array}{l}\mathbf{V\;=\;-\;\frac{GM}{R^{3}}\;\left [ \frac{R^{2}}{2} \;-\;\frac{r^{2}}{6} \right ]}\end{array} \)

Escape Velocity

The escape velocity is the minimum velocity given to an object to make it free from the gravitational field. Let veย be the escape velocity of the body and m be the mass of the object to be projected, then,

\(\begin{array}{l}\mathbf{v_{e}\;=\;\sqrt{\frac{2\;G\; M}{R}}}\end{array} \)

Escape velocity

 

Read More:ย Escape and Orbital Velocity

To learn more about gravity and the forces attached to it, visit BYJU’S website or download BYJU’S – The Learning App. On our website, you can access more details om JEE, JEE syllabus, JEE preparation tips, JEE books and more.

Kepler’s Laws of Planetary Motion

Frequently Asked Questions on Gravity

Q1

Give two examples of central force.

  1. Gravitational force
  2. The electrostatic force between two point charges
Q2

Suppose the two-point charges are dipped inside water. How is the gravitational force between the two-point charges affected?

The gravitational force between the two-point charges does not depend upon the nature of the medium. Therefore, gravitational force will not get affected.

Q3

A charge can be shielded from the influence of the external electric field by putting it into a hollow cylinder. Can a body be shielded from the gravitational influence of nearby matter by putting it in a hollow sphere or by any other method?

Gravitational force is independent of the intervening medium; therefore, the body cannot be shielded from the gravitational influence of nearby matter by placing it in a hollow cylinder.

Q4

Is it possible for an object to have inertia but not weight?

Inertia is the mass of the body. When the body is taken to the centre of the earth, the weight (mg) of the body will be zero, but the body will still have mass.

Test Your Knowledge On Gravity!

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