NEET Exam > NEET Questions > The distance between sun and a planet is r. T...
Start Learning for Free
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=?
Most Upvoted Answer
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.
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Top Courses for NEETView all
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=?
Question Description
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=?.
Solutions 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=? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of 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=? defined & explained in the simplest way possible. Besides giving the explanation of
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=?, a detailed solution 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=? has been provided alongside types of 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=? theory, EduRev gives you an
ample number of questions to practice 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=? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup