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, gravitation forms a crucial chapter as it explains the universal force responsible for planetary motions, tides, and weight.

Key points:

• Gravitation acts between any two masses regardless of their state.
• It is a long-range force, meaning it acts over large distances.
• Understanding gravitation helps explain phenomena like orbits and free fall.

This chapter lays the foundation for higher studies in mechanics and astrophysics, making it essential for CBSE exams.

Newton’s Law of Universal Gravitation Explained

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

Mathematically:

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

Where:

• $F$ = gravitational force between two masses
• $m_1$, $m_2$ = masses of the objects
• $r$ = distance between the centers of the two masses
• $G$ = universal gravitational constant ($6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$)

This formula helps calculate the gravitational force acting between any two bodies, from apples falling to planets orbiting the sun.

Acceleration Due to Gravity and Its Variation

Acceleration due to gravity ($g$) is the acceleration experienced by an object due to Earth's gravitational pull.

Formula:

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

Where:

• $G$ = gravitational constant
• $M$ = mass of Earth
• $R$ = radius of Earth

Key points about $g$:

• Standard value of $g$ on Earth’s surface is approximately 9.8 m/s².
• $g$ decreases with altitude and increases slightly below Earth's surface.
• Variation affects weight and free-fall motion.

Understanding these variations is important for solving problems related to weight and motion in Class 11 Physics.

Gravitational Potential and Potential Energy

Gravitational potential at a point is defined as the work done per unit mass in bringing a small mass from infinity to that point.

Formula for gravitational potential $V$:

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

Where $r$ is the distance from the center of the Earth or mass causing the field.

Gravitational potential energy ($U$) of a mass $m$ at distance $r$:

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

Key notes:

• Potential is negative, indicating work is done by the gravitational force.
• Potential energy decreases (becomes more negative) as the object moves closer to the mass.

These concepts help explain energy changes in satellite motion and free fall.

Comparison: Gravitational Force vs Other Fundamental Forces

Here’s a quick comparison of gravitational force with other fundamental forces:

Understanding gravitation’s unique properties helps Class 11 students appreciate its role in the universe.

Worked Example: Calculating Gravitational Force Between Two Masses

Example: Calculate the gravitational force between two masses of 5 kg and 10 kg placed 2 meters apart.

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:

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

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

So, the gravitational force is approximately $8.34 \times 10^{-10}$ Newtons.

This example illustrates how gravitational forces, though universal, are very weak between small masses.