Summary force and motion class 10

Title
Science – Unit 7: Force and Motion – Nepal Curriculum, SEE Examination – Complete
Study Notes on Gravitation and Gravity

Description
These complete study notes cover the gravitation and gravity topics of Unit 7: Force and
Motion for Science under the Nepal curriculum. The material includes Newton’s universal
law of gravitation, the universal gravitational constant, acceleration due to gravity,
variation in gravity, mass and weight, free fall, weightlessness, and the effects of
gravitation.

The notes are designed for SEE examination preparation and include important
definitions, mathematical derivations, formulas, solved numerical problems, differences
between key concepts, revision points, and practice questions with answers. They
provide a structured resource for understanding the chapter, revising essential concepts,
and practicing common examination questions.

Complete Study Notes: Unit 7 – Force and Motion
1. Introduction to Gravitation
Gravitation is the natural force of attraction between any two objects having mass in the
universe.

Every object attracts every other object because of its mass. However, the gravitational
force between ordinary objects is usually too small to notice in everyday life.

Examples of gravitation
The Earth attracts objects towards its surface.
The Moon revolves around the Earth due to gravitational attraction.
The planets revolve around the Sun.
The Sun and Moon contribute to ocean tides.
Artificial satellites remain in orbit around the Earth due to gravity.
Importance of gravitation
1. It keeps planets in their orbits around the Sun.
2. It keeps the Moon and artificial satellites in orbit around the Earth.
3. It holds the atmosphere around the Earth.

, 4. It causes objects to fall towards the Earth's surface.
5. It contributes to ocean tides through the gravitational attraction of the Moon and
Sun.

2. Newton’s Universal Law of Gravitation
Sir Isaac Newton formulated the universal law of gravitation to explain the gravitational
attraction between objects.

Statement of the law
Every object in the universe attracts every other object with a force that is directly
proportional to the product of their masses and inversely proportional to the square of the
distance between their centres.

Mathematical derivation
Let:

(F) = gravitational force between two objects
(m_1) = mass of the first object
(m_2) = mass of the second object
(d) = distance between the centres of the objects
(G) = universal gravitational constant
According to the law:

Step 1: Force is directly proportional to the product of the masses.

[
F\propto m_1m_2
]

Step 2: Force is inversely proportional to the square of the distance.

[
F\propto \frac{1}{d^2}
]

Combining both relationships:

[
F\propto \frac{m_1m_2}{d^2}
]

Introducing the proportionality constant (G):

, [
\boxed{F=G\frac{m_1m_2}{d^2}}
]

This is the mathematical expression of Newton’s universal law of gravitation.

Factors affecting gravitational force
Mass: Increasing either mass increases the gravitational force.
Distance: Increasing the distance between the centres decreases the
gravitational force.
Universal gravitational constant: The value of (G) is constant for gravitational
interactions.

Relationship between force and distance
If the distance is doubled:

[
F'=\frac{F}{4}
]

If the distance is tripled:

[
F'=\frac{F}{9}
]

If the distance is halved:

[
F'=4F
]

If either one of the masses is doubled, the force doubles. If both masses are doubled,
the force becomes four times as large, provided the distance remains unchanged.

3. Universal Gravitational Constant (G)
Definition
The universal gravitational constant is the proportionality constant in Newton’s universal
law of gravitation. Numerically, it equals the gravitational force between two point
masses of 1 kg each separated by 1 m in a vacuum.

Value