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Time period of revolution of a satellite around a planet of radius R is T. Period ofrevolution around another planet, whose radius is 3R but having same density is: (1) T/(3sqrt(3)) (2) 3T (3) 9T (4) 3sqrt(3) * T?
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Time period of revolution of a satellite around a planet of radius R i...
Given:
- Radius of the first planet = R
- Time period of revolution around the first planet = T
To find:
- Time period of revolution around the second planet (with radius 3R) having the same density
Formula:
The formula for the time period of revolution of a satellite around a planet is given by:
T = 2π√(R³/GM)
Where:
T = Time period of revolution
R = Radius of the planet
G = Universal gravitational constant
M = Mass of the planet
Explanation:
1. We are given the time period of revolution around the first planet as T.
2. The time period of revolution of a satellite around a planet depends on the radius and mass of the planet.
3. Let's assume the mass of both the planets is the same because they have the same density.
4. We know that the radius of the second planet is 3R, which means it is three times larger than the first planet.
5. Substituting the values in the formula, we have:
T₁ = 2π√(R³/GM) (Time period around the first planet)
T₂ = 2π√((3R)³/GM) (Time period around the second planet)
6. Simplifying the equation for T₂, we get:
T₂ = 2π√(27R³/GM)
T₂ = 3√3 * 2π√(R³/GM)
T₂ = 3√3 * T₁
Therefore, the time period of revolution around the second planet is 3√3 times the time period around the first planet.
Answer:
The correct option is (4) 3√3 * T.
- Radius of the first planet = R
- Time period of revolution around the first planet = T
To find:
- Time period of revolution around the second planet (with radius 3R) having the same density
Formula:
The formula for the time period of revolution of a satellite around a planet is given by:
T = 2π√(R³/GM)
Where:
T = Time period of revolution
R = Radius of the planet
G = Universal gravitational constant
M = Mass of the planet
Explanation:
1. We are given the time period of revolution around the first planet as T.
2. The time period of revolution of a satellite around a planet depends on the radius and mass of the planet.
3. Let's assume the mass of both the planets is the same because they have the same density.
4. We know that the radius of the second planet is 3R, which means it is three times larger than the first planet.
5. Substituting the values in the formula, we have:
T₁ = 2π√(R³/GM) (Time period around the first planet)
T₂ = 2π√((3R)³/GM) (Time period around the second planet)
6. Simplifying the equation for T₂, we get:
T₂ = 2π√(27R³/GM)
T₂ = 3√3 * 2π√(R³/GM)
T₂ = 3√3 * T₁
Therefore, the time period of revolution around the second planet is 3√3 times the time period around the first planet.
Answer:
The correct option is (4) 3√3 * T.
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Time period of revolution of a satellite around a planet of radius R is T. Period ofrevolution around another planet, whose radius is 3R but having same density is: (1) T/(3sqrt(3)) (2) 3T (3) 9T (4) 3sqrt(3) * T?
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Time period of revolution of a satellite around a planet of radius R is T. Period ofrevolution around another planet, whose radius is 3R but having same density is: (1) T/(3sqrt(3)) (2) 3T (3) 9T (4) 3sqrt(3) * T? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Time period of revolution of a satellite around a planet of radius R is T. Period ofrevolution around another planet, whose radius is 3R but having same density is: (1) T/(3sqrt(3)) (2) 3T (3) 9T (4) 3sqrt(3) * T? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Time period of revolution of a satellite around a planet of radius R is T. Period ofrevolution around another planet, whose radius is 3R but having same density is: (1) T/(3sqrt(3)) (2) 3T (3) 9T (4) 3sqrt(3) * T?.
Time period of revolution of a satellite around a planet of radius R is T. Period ofrevolution around another planet, whose radius is 3R but having same density is: (1) T/(3sqrt(3)) (2) 3T (3) 9T (4) 3sqrt(3) * T? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Time period of revolution of a satellite around a planet of radius R is T. Period ofrevolution around another planet, whose radius is 3R but having same density is: (1) T/(3sqrt(3)) (2) 3T (3) 9T (4) 3sqrt(3) * T? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Time period of revolution of a satellite around a planet of radius R is T. Period ofrevolution around another planet, whose radius is 3R but having same density is: (1) T/(3sqrt(3)) (2) 3T (3) 9T (4) 3sqrt(3) * T?.
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