What is Gravitation Class 11 Notes: Complete Physics Guide

Definition and Importance of Gravitation in Class 11 Physics

Gravitation is a natural phenomenon by which all objects with mass attract each other. In Class 11 NCERT Physics, this concept forms the foundation for understanding planetary motion, satellite dynamics, and forces acting on bodies on Earth.

Key points:

• Gravitation acts between any two masses regardless of their size.
• It is a universal force, meaning it works everywhere in the universe.
• Understanding gravitation helps in explaining tides, orbits, and weight.

This chapter is crucial for CBSE exams as it links theoretical concepts with practical examples.

Newton’s Law of Universal Gravitation Explained

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

The formula is:

$$F = G \frac{m_1 m_2}{r^2}$$

Where:

• $F$ is the gravitational force
• $G$ is the gravitational constant ($6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$)
• $m_1$ and $m_2$ are the masses
• $r$ is the distance between the masses

This law helps calculate the force between planets, satellites, and objects on Earth.

Gravitational Acceleration and Its Calculation

Gravitational acceleration ($g$) is the acceleration experienced by an object due to Earth’s gravity.

Formula:

$$g = \frac{GM}{R^2}$$

Where:

• $G$ is the gravitational constant
• $M$ is the mass of Earth
• $R$ is the radius of Earth

Near Earth's surface, $g$ is approximately 9.8 m/s². This acceleration causes objects to fall freely.

Example: Calculate $g$ if $M = 5.97 \times 10^{24}$ kg and $R = 6.37 \times 10^6$ m.

$$g = \frac{6.674 \times 10^{-11} \times 5.97 \times 10^{24}}{(6.37 \times 10^6)^2} = 9.8 \, m/s^2$$

Gravitational Potential and Potential Energy

Gravitational potential ($V$) at a point is the work done per unit mass in bringing a mass from infinity to that point.

Formula:

$$V = -\frac{GM}{r}$$

Gravitational potential energy ($U$) of a mass $m$ at distance $r$ from Earth’s centre is:

$$U = mV = -\frac{GMm}{r}$$

The negative sign indicates that work is done against the gravitational field to move the mass away.

Understanding potential energy helps in satellite motion and energy conservation.

Comparison: Gravitational Force vs Other Fundamental Forces

Gravitation is unique due to its universal attraction and infinite range.

Kepler’s Laws and Their Relation to Gravitation

Kepler’s laws describe planetary motion, derived from gravitation:

1. Law of Orbits: Planets move in elliptical orbits with the Sun at one focus. 2. Law of Areas: A line joining a planet and the Sun sweeps equal areas in equal times. 3. Law of Periods: The square of the orbital period is proportional to the cube of the semi-major axis.

Mathematically:

$$T^2 \propto r^3$$

Where $T$ is the orbital period and $r$ is the average distance from the Sun.

These laws are explained by Newton’s law of gravitation and help in understanding satellite orbits.

Solved Example: Calculating Gravitational Force Between Two Masses

Problem: Two masses, 5 kg and 10 kg, are 2 meters apart. Calculate the gravitational force between them.

Solution:

Given:

• $m_1 = 5$ kg
• $m_2 = 10$ kg
• $r = 2$ m
• $G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$

Using Newton’s law:

$$F = G \frac{m_1 m_2}{r^2} = 6.674 \times 10^{-11} \times \frac{5 \times 10}{2^2}$$

$$F = 6.674 \times 10^{-11} \times \frac{50}{4} = 6.674 \times 10^{-11} \times 12.5 = 8.3425 \times 10^{-10} \, N$$

The gravitational force is approximately $8.34 \times 10^{-10}$ Newtons, very small but always present.