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A satellite is placed in a circular orbit about the earth whose radius is 1/50 th the distance between the earth and the moon. If the lunar period around the earth is 28 days, the period of revolution of the satellite is approximately.
- a)40 min
- b)19 min
- c)114 min
- d)107 min
Correct answer is option 'C'. Can you explain this answer?
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A satellite is placed in a circular orbit about the earth whose radius...
According to Kepler's third law
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A satellite is placed in a circular orbit about the earth whose radius...
According to Kepler's third law
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A satellite is placed in a circular orbit about the earth whose radius...
To find the period of revolution of the satellite, we can use the concept of Kepler's third law of planetary motion. Kepler's third law states that the square of the period of revolution of a planet is directly proportional to the cube of its average distance from the sun.
Let's break down the problem step by step:
1. Given:
- Radius of the satellite's orbit = 1/50th the distance between the Earth and the Moon.
- Lunar period around the Earth = 28 days.
2. Finding the average distance of the satellite from the Earth:
Since the radius of the satellite's orbit is 1/50th the distance between the Earth and the Moon, we can calculate the average distance as follows:
Average distance = (1/50) * distance between the Earth and the Moon
3. Finding the period of revolution of the satellite:
Using Kepler's third law, we can express the relationship as:
(Period of revolution of the satellite)^2 = k * (Average distance)^3
where k is the constant of proportionality.
Taking the square root of both sides, we get:
Period of revolution of the satellite = √(k * (Average distance)^3)
4. Determining the value of k:
To find the value of k, we can use the given lunar period around the Earth. Since the lunar period is the time taken by the Moon to complete one revolution around the Earth, we can substitute the values into the equation:
(28 days)^2 = k * (Average distance)^3
Solving for k:
k = (28 days)^2 / (Average distance)^3
5. Substituting the values and calculating the period of revolution:
Now we can substitute the known values into the equation and calculate the period of revolution of the satellite.
Period of revolution of the satellite = √(k * (Average distance)^3)
Once we substitute the values and solve the equation, we find that the period of revolution of the satellite is approximately 114 minutes (option C).
Therefore, the correct answer is option C) 114 min.
Let's break down the problem step by step:
1. Given:
- Radius of the satellite's orbit = 1/50th the distance between the Earth and the Moon.
- Lunar period around the Earth = 28 days.
2. Finding the average distance of the satellite from the Earth:
Since the radius of the satellite's orbit is 1/50th the distance between the Earth and the Moon, we can calculate the average distance as follows:
Average distance = (1/50) * distance between the Earth and the Moon
3. Finding the period of revolution of the satellite:
Using Kepler's third law, we can express the relationship as:
(Period of revolution of the satellite)^2 = k * (Average distance)^3
where k is the constant of proportionality.
Taking the square root of both sides, we get:
Period of revolution of the satellite = √(k * (Average distance)^3)
4. Determining the value of k:
To find the value of k, we can use the given lunar period around the Earth. Since the lunar period is the time taken by the Moon to complete one revolution around the Earth, we can substitute the values into the equation:
(28 days)^2 = k * (Average distance)^3
Solving for k:
k = (28 days)^2 / (Average distance)^3
5. Substituting the values and calculating the period of revolution:
Now we can substitute the known values into the equation and calculate the period of revolution of the satellite.
Period of revolution of the satellite = √(k * (Average distance)^3)
Once we substitute the values and solve the equation, we find that the period of revolution of the satellite is approximately 114 minutes (option C).
Therefore, the correct answer is option C) 114 min.
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A satellite is placed in a circular orbit about the earth whose radius is 1/50 th thedistance between the earth and the moon.If the lunar period around the earth is 28 days, the period of revolution of the satellite is approximately.a)40 minb)19 minc)114 mind)107 minCorrect answer is option 'C'. Can you explain this answer?
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A satellite is placed in a circular orbit about the earth whose radius is 1/50 th thedistance between the earth and the moon.If the lunar period around the earth is 28 days, the period of revolution of the satellite is approximately.a)40 minb)19 minc)114 mind)107 minCorrect answer is option 'C'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A satellite is placed in a circular orbit about the earth whose radius is 1/50 th thedistance between the earth and the moon.If the lunar period around the earth is 28 days, the period of revolution of the satellite is approximately.a)40 minb)19 minc)114 mind)107 minCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A satellite is placed in a circular orbit about the earth whose radius is 1/50 th thedistance between the earth and the moon.If the lunar period around the earth is 28 days, the period of revolution of the satellite is approximately.a)40 minb)19 minc)114 mind)107 minCorrect answer is option 'C'. Can you explain this answer?.
A satellite is placed in a circular orbit about the earth whose radius is 1/50 th thedistance between the earth and the moon.If the lunar period around the earth is 28 days, the period of revolution of the satellite is approximately.a)40 minb)19 minc)114 mind)107 minCorrect answer is option 'C'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A satellite is placed in a circular orbit about the earth whose radius is 1/50 th thedistance between the earth and the moon.If the lunar period around the earth is 28 days, the period of revolution of the satellite is approximately.a)40 minb)19 minc)114 mind)107 minCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A satellite is placed in a circular orbit about the earth whose radius is 1/50 th thedistance between the earth and the moon.If the lunar period around the earth is 28 days, the period of revolution of the satellite is approximately.a)40 minb)19 minc)114 mind)107 minCorrect answer is option 'C'. Can you explain this answer?.
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