What is Gravitation Class 11: Definition and Key Concepts Explained

Definition and Importance of Gravitation in Class 11 Physics

Gravitation is a fundamental force that causes every object in the universe to attract every other object with a force that depends on their masses and the distance between them. In Class 11 NCERT Physics, gravitation is introduced as the force responsible for keeping planets in orbit, causing objects to fall on Earth, and governing the motion of celestial bodies.

Key points:

• Gravitation acts between any two masses.
• It is always attractive.
• It acts along the line joining the centres of the two masses.

Understanding gravitation helps explain natural phenomena like tides, planetary orbits, and weight variations on Earth.

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.

Mathematically, the gravitational force $F$ between two masses $m_1$ and $m_2$ separated by distance $r$ is:

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

Where:

• $G$ is the universal gravitational constant ($6.674 \times 10^{-11} \, N\, m^2/kg^2$)

This law is universal and applies to all objects with mass, from apples falling to planets orbiting the sun.

Worked example: Calculate the gravitational force between two 5 kg masses placed 2 m apart.

$$ F = 6.674 \times 10^{-11} \times \frac{5 \times 5}{2^2} = 6.674 \times 10^{-11} \times \frac{25}{4} = 4.17 \times 10^{-10} \, N $$

Gravitational Field and Acceleration Due to Gravity

The gravitational field at a point is the gravitational force experienced by a unit mass placed at that point. It is a vector quantity.

The acceleration due to gravity $g$ near the Earth's surface is approximately $9.8 \, m/s^2$, directed towards the Earth's centre.

Formula for $g$:

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

Where:

• $M$ is Earth's mass
• $R$ is Earth's radius

Variation of $g$:

• $g$ decreases with altitude above Earth’s surface.
• $g$ decreases slightly below Earth’s surface.

This section is crucial for understanding weight and motion in gravitational fields.

Gravitational Potential and Potential Energy

Gravitational potential at a point is the work done per unit mass in bringing a mass from infinity to that point in a gravitational field.

It is a scalar quantity and given by:

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

Where $r$ is the distance from the centre of the Earth or any other mass.

Gravitational potential energy (GPE) is the energy possessed by a mass due to its position in a gravitational field:

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

This negative value indicates that work must be done against gravity to move a mass away from the Earth.

Example: Calculate the GPE of a 10 kg object at 10 m above Earth's surface.

Assuming $g = 9.8 \, m/s^2$ and $R = 6.4 \times 10^6 \, m$,

$$ U = mg h = 10 \times 9.8 \times 10 = 980 \, J $$

This approximation is valid near Earth's surface.

Difference Between Gravitational Force and Other Fundamental Forces

Gravitational force is one of the four fundamental forces of nature. Here's how it compares with others:

Gravitation governs large-scale phenomena like planetary motion, while other forces dominate atomic and subatomic interactions.

Applications of Gravitation in Daily Life and Astronomy

Gravitation affects many aspects of daily life and the universe:

• Objects fall to Earth: Gravity pulls objects downwards.
• Tides: Gravitational pull of the moon causes ocean tides.
• Planetary orbits: Gravity keeps planets revolving around the sun.
• Weight measurement: Weight is the force due to gravity on a mass.
• Satellite motion: Satellites stay in orbit due to Earth's gravity.

Understanding gravitation helps in designing satellites, predicting tides, and explaining natural phenomena.

This knowledge is essential for Class 11 students preparing for board exams and competitive tests.