NEET Exam > NEET Questions > The density of a newly discovered planet is t...
Start Learning for Free
The density of a newly discovered planet is twice the earth. the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. if the radius of earth is R, then radius of the planet would be?
Most Upvoted Answer
The density of a newly discovered planet is twice the earth. the accel...
Explanation:
Let the radius and density of the newly discovered planet be R' and ρ' respectively. Given that density of planet is twice the earth. So,
ρ' = 2ρ
where ρ is the density of earth.
Acceleration due to gravity at the surface of planet:
From the given information, we know that the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. This can be represented as:
G(M'/R'^2) = G(M/R^2)
where G is the gravitational constant, M' and M are the masses of the planet and earth respectively.
Calculation of radius of planet:
We can calculate the radius of the planet using the above equation as:
(M'/R'^2) = (M/R^2)
or
(M'/M) = (R'^2/R^2)
Since the density of planet is twice that of earth, we can write:
(M'/M) = (4/3)πρ'R'^3 / (4/3)πρR^3
or
(M'/M) = (ρ'R'^3 / ρR^3)
Substituting the value of (M'/M) in the earlier equation, we get:
(ρ'R'^3 / ρR^3) = (R'^2/R^2)
or
R' = R(ρ'/ρ)^(1/3)
Substituting the values of ρ' and ρ, we get:
R' = R(2)^(1/3)
Therefore, the radius of the newly discovered planet is R(2)^(1/3) times that of the earth.
Let the radius and density of the newly discovered planet be R' and ρ' respectively. Given that density of planet is twice the earth. So,
ρ' = 2ρ
where ρ is the density of earth.
Acceleration due to gravity at the surface of planet:
From the given information, we know that the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. This can be represented as:
G(M'/R'^2) = G(M/R^2)
where G is the gravitational constant, M' and M are the masses of the planet and earth respectively.
Calculation of radius of planet:
We can calculate the radius of the planet using the above equation as:
(M'/R'^2) = (M/R^2)
or
(M'/M) = (R'^2/R^2)
Since the density of planet is twice that of earth, we can write:
(M'/M) = (4/3)πρ'R'^3 / (4/3)πρR^3
or
(M'/M) = (ρ'R'^3 / ρR^3)
Substituting the value of (M'/M) in the earlier equation, we get:
(ρ'R'^3 / ρR^3) = (R'^2/R^2)
or
R' = R(ρ'/ρ)^(1/3)
Substituting the values of ρ' and ρ, we get:
R' = R(2)^(1/3)
Therefore, the radius of the newly discovered planet is R(2)^(1/3) times that of the earth.
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
|
|
Similar NEET Doubts
Top Courses for NEETView all
The density of a newly discovered planet is twice the earth. the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. if the radius of earth is R, then radius of the planet would be?
Question Description
The density of a newly discovered planet is twice the earth. the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. if the radius of earth is R, then radius of the planet would be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The density of a newly discovered planet is twice the earth. the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. if the radius of earth is R, then radius of the planet would be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The density of a newly discovered planet is twice the earth. the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. if the radius of earth is R, then radius of the planet would be?.
The density of a newly discovered planet is twice the earth. the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. if the radius of earth is R, then radius of the planet would be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The density of a newly discovered planet is twice the earth. the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. if the radius of earth is R, then radius of the planet would be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The density of a newly discovered planet is twice the earth. the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. if the radius of earth is R, then radius of the planet would be?.
Solutions for The density of a newly discovered planet is twice the earth. the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. if the radius of earth is R, then radius of the planet would be? 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 density of a newly discovered planet is twice the earth. the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. if the radius of earth is R, then radius of the planet would be? defined & explained in the simplest way possible. Besides giving the explanation of
The density of a newly discovered planet is twice the earth. the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. if the radius of earth is R, then radius of the planet would be?, a detailed solution for The density of a newly discovered planet is twice the earth. the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. if the radius of earth is R, then radius of the planet would be? has been provided alongside types of The density of a newly discovered planet is twice the earth. the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. if the radius of earth is R, then radius of the planet would be? theory, EduRev gives you an
ample number of questions to practice The density of a newly discovered planet is twice the earth. the acceleration due to gravity at the surface of planet is equal to that at the surface of the earth. if the radius of earth is R, then radius of the planet would be? 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup