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An artificial satellite is moving in a circular orbit around the Earth at a height R from the surface of the Earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on the Earth, the speed with which it will hit the surface of the Earth will be?
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An artificial satellite is moving in a circular orbit around the Earth...
Explanation of the problem
An artificial satellite moving in a circular orbit around the Earth at a height R from the surface of the Earth has a certain speed that keeps it in orbit. If the satellite is suddenly stopped in its orbit, it will fall freely towards the Earth due to gravity. The question is asking for the speed with which it will hit the surface of the Earth.
Deriving the formula to calculate the speed
To calculate the speed with which the satellite will hit the Earth, we need to apply the law of conservation of energy. When the satellite is in orbit, it has a certain amount of kinetic energy and potential energy due to its height from the surface of the Earth. When it falls freely towards the Earth, its potential energy is converted into kinetic energy. Using the conservation of energy equation, we can equate the initial potential energy of the satellite to its final kinetic energy as it hits the Earth.
Initial potential energy = Final kinetic energy
mgR = 1/2 mv^2
where m = mass of the satellite, g = acceleration due to gravity, R = distance from the center of the Earth to the satellite, and v = final velocity of the satellite as it hits the Earth.
Simplifying the equation,
v = sqrt(2gR)
Calculating the speed
Using the above formula, we can calculate the speed with which the satellite will hit the surface of the Earth.
Assuming R = 6371 km (radius of the Earth), g = 9.81 m/s^2 (acceleration due to gravity),
v = sqrt(2 x 9.81 m/s^2 x 6371 km x 1000 m/km) = 11.2 km/s
Conclusion
The speed with which the satellite will hit the surface of the Earth if it is suddenly stopped in its orbit and allowed to fall freely is approximately 11.2 km/s. This is a very high speed and the impact would be catastrophic. However, in reality, most satellites are designed to burn up in the Earth's atmosphere before hitting the surface.
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An artificial satellite is moving in a circular orbit around the Earth at a height R from the surface of the Earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on the Earth, the speed with which it will hit the surface of the Earth will be?
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An artificial satellite is moving in a circular orbit around the Earth at a height R from the surface of the Earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on the Earth, the speed with which it will hit the surface of the Earth will be? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An artificial satellite is moving in a circular orbit around the Earth at a height R from the surface of the Earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on the Earth, the speed with which it will hit the surface of the Earth will be? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An artificial satellite is moving in a circular orbit around the Earth at a height R from the surface of the Earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on the Earth, the speed with which it will hit the surface of the Earth will be?.
An artificial satellite is moving in a circular orbit around the Earth at a height R from the surface of the Earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on the Earth, the speed with which it will hit the surface of the Earth will be? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An artificial satellite is moving in a circular orbit around the Earth at a height R from the surface of the Earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on the Earth, the speed with which it will hit the surface of the Earth will be? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An artificial satellite is moving in a circular orbit around the Earth at a height R from the surface of the Earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on the Earth, the speed with which it will hit the surface of the Earth will be?.
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