Derive universal law of gravitation ?

Question

Answer

Its states that the force of attraction b/w two bodies is directly proportional to thier product of masses n inversely proportional to the square of the distance b/w them

Answer

This law is applicable only if the following Conditions are met..

1 - Two Bodies having Mass
2 - There must be Some Distance between them

According to Universal Gravitional Law :

(i)The Gravitional force Between two bodies having mass m1 and m2 directly depends on the product of their masses and

(ii) Inversely Proportional to the Square of distance between them...

F = Gravitional force
m1 and m2 are the masses of bodies
r = Distance between the bodies having masses m1 and m2...

Now from statement (i) and (ii) we must have

F = G m1 x m2 / r^2 ----(iii) where G is the constant of proportionality..called Universal gravitional Constant.....
According to relation (iii)..if mass of the body increases then F will increase too...and decreases if the distance between them increases...

Answer

Derivation of the Universal Law of Gravitation

The Universal Law of Gravitation was formulated by Sir Isaac Newton and is a fundamental principle in physics that describes the force of gravity between two objects. This law states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Key Points:
- Universal Law of Gravitation: Every particle attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
- Formulated by Sir Isaac Newton.
- Describes the force of gravity between two objects.

Newton's Law of Universal Gravitation Equation:
The equation for the Universal Law of Gravitation is given as:

F = G * (m1 * m2) / r^2

Where:
- F represents the gravitational force between the two objects.
- G is the gravitational constant, which has a value of approximately 6.674 × 10^-11 N (m/kg)^2.
- m1 and m2 are the masses of the two objects.
- r is the distance between the centers of the two objects.

Derivation:
To derive the Universal Law of Gravitation, consider two objects with masses m1 and m2, separated by a distance r. The force of gravity between them can be determined by considering the acceleration experienced by each object due to the gravitational force.

1. According to Newton's second law of motion, the force acting on an object is equal to its mass multiplied by its acceleration (F = m * a).
2. The acceleration due to gravity is given by the equation a = F_gravity / m, where F_gravity is the gravitational force acting on the object and m is its mass.
3. The gravitational force can be expressed as F_gravity = G * (m1 * m2) / r^2, where G is the gravitational constant.
4. Substituting this expression for F_gravity in the equation for acceleration, we get a = G * (m1 * m2) / (m * r^2).
5. Since both masses experience the same acceleration, we can equate the two expressions for acceleration and cancel out the mass terms.
6. This leads to the equation G * (m1 * m2) / (r^2) = G * (m2 * m1) / (r^2) = a.
7. Therefore, the gravitational force F_gravity between the two objects is proportional to the product of their masses (m1 * m2) and inversely proportional to the square of the distance between them (r^2).

Conclusion:
By deriving the Universal Law of Gravitation, we have shown that the force of gravity between two objects can be described using the equation F = G * (m1 * m2) / r^2. This law is essential for understanding and calculating the gravitational interactions between celestial bodies, as well as various phenomena on Earth.

Similar Class 9 Doubts

Is the moon attracts the earth , why does the earth not move towards the moon? Related: Newton's Universal Law of Gravitation and Gravitational Force - Gravitation, Class 9, Science

what is gravitational Related: Newton's Universal Law of Gravitation and Gravitational Force?

Needed a Document for gravitation? Related: Newton's Universal Law of Gravitation and Gravitational Force?

State universal law of Gravitation. Give the mathematical expression for Universal law of gravitation. Explain its irnportance.?

Why universal law of gravitation called universal?

Top Courses for Class 9View all

Science Class 9

Social Studies (SST) Class 9

Mathematics (Maths) Class 9

English Grammar Advanced

English Class 9

Top Courses for Class 9

Top Courses for Class 9

Suggested Free Tests

Related Content

Class 9 Study Material

Class 9 Subjects

Competitive Examinations for Class 9

NCERT Books

NCERT Solutions

Reference Books for Class 9

Other Popular Exams

Company