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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?
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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.
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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?
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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?.
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