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The distance between sun and a planet is r. The angular momentum of planet around the sun in circular orbit is propertional to r^n,then,n=?
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The distance between sun and a planet is r. The angular momentum of pl...
Angular Momentum in Circular Orbit
Angular momentum is a measure of the rotational motion of an object around a point or axis. In the case of a planet orbiting the Sun, the angular momentum is the product of the planet's moment of inertia and its angular velocity.
Angular Momentum Formula
The formula for angular momentum is given by:
L = Iω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
Relationship with Distance
In a circular orbit, the moment of inertia can be expressed as:
I = mr^2
where m is the mass of the planet and r is the distance between the planet and the Sun.
Proportional Relationship
According to the question, the angular momentum is proportional to r^n. Therefore, we can write:
L ∝ r^n
Substituting the expressions for L and I, we have:
mr^2ω ∝ r^n
Mass and Angular Velocity
The mass of the planet and the angular velocity remain constant for a given planet. Therefore, we can write:
mω ∝ r^n-2
Deducing the Value of n
Comparing the powers of r on both sides of the equation, we get:
n - 2 = 1
n = 3
Conclusion
The value of n is 3. This means that the angular momentum of a planet around the Sun in a circular orbit is proportional to the cube of the distance between them.
Angular momentum is a measure of the rotational motion of an object around a point or axis. In the case of a planet orbiting the Sun, the angular momentum is the product of the planet's moment of inertia and its angular velocity.
Angular Momentum Formula
The formula for angular momentum is given by:
L = Iω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
Relationship with Distance
In a circular orbit, the moment of inertia can be expressed as:
I = mr^2
where m is the mass of the planet and r is the distance between the planet and the Sun.
Proportional Relationship
According to the question, the angular momentum is proportional to r^n. Therefore, we can write:
L ∝ r^n
Substituting the expressions for L and I, we have:
mr^2ω ∝ r^n
Mass and Angular Velocity
The mass of the planet and the angular velocity remain constant for a given planet. Therefore, we can write:
mω ∝ r^n-2
Deducing the Value of n
Comparing the powers of r on both sides of the equation, we get:
n - 2 = 1
n = 3
Conclusion
The value of n is 3. This means that the angular momentum of a planet around the Sun in a circular orbit is proportional to the cube of the distance between them.
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The distance between sun and a planet is r. The angular momentum of planet around the sun in circular orbit is propertional to r^n,then,n=?
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The distance between sun and a planet is r. The angular momentum of planet around the sun in circular orbit is propertional to r^n,then,n=? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The distance between sun and a planet is r. The angular momentum of planet around the sun in circular orbit is propertional to r^n,then,n=? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The distance between sun and a planet is r. The angular momentum of planet around the sun in circular orbit is propertional to r^n,then,n=?.
The distance between sun and a planet is r. The angular momentum of planet around the sun in circular orbit is propertional to r^n,then,n=? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The distance between sun and a planet is r. The angular momentum of planet around the sun in circular orbit is propertional to r^n,then,n=? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The distance between sun and a planet is r. The angular momentum of planet around the sun in circular orbit is propertional to r^n,then,n=?.
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