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A satellite is moving round the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1% then what is its speed. Option- a) increases 1%, b) increases 0.5%, c) decreases 1%, d) decreases 0.5%
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A satellite is moving round the earth with speed v in a circular orbit...
Understanding Satellite Speed in Circular Orbits
When a satellite moves in a circular orbit around the Earth, its speed is determined by the gravitational force acting on it. The centripetal force required to keep the satellite in orbit is provided by this gravitational force.
Initial Speed Calculation
- The gravitational force provides the necessary centripetal force:
F = (mv^2)/r = GMm/r²
- Here, G is the gravitational constant, M is the mass of the Earth, and m is the mass of the satellite.
- Rearranging gives us the orbital speed:
v = √(GM/r)
Effect of Decreasing the Orbit Radius
If the radius r is decreased by 1%, the new radius, r', can be expressed as:
- r' = r - 0.01r = 0.99r
New Speed Calculation
- The new speed v' becomes:
v' = √(GM/r')
- Substituting r' into the equation gives:
v' = √(GM/(0.99r))
Speed Comparison
- This simplifies to:
v' = √(GM/r) * √(1/0.99)
- Notably, since √(1/0.99) is greater than 1, we find that:
v' > v
Percentage Increase in Speed
- The percentage increase in speed can be calculated as:
(v' - v)/v * 100
- Since √(1/0.99) is approximately 1.005, the speed increases by roughly 0.5%.
Conclusion
The speed of the satellite increases by approximately 0.5% when the orbit radius is decreased by 1%. Thus, the correct option is:
Option: b) increases 0.5%
When a satellite moves in a circular orbit around the Earth, its speed is determined by the gravitational force acting on it. The centripetal force required to keep the satellite in orbit is provided by this gravitational force.
Initial Speed Calculation
- The gravitational force provides the necessary centripetal force:
F = (mv^2)/r = GMm/r²
- Here, G is the gravitational constant, M is the mass of the Earth, and m is the mass of the satellite.
- Rearranging gives us the orbital speed:
v = √(GM/r)
Effect of Decreasing the Orbit Radius
If the radius r is decreased by 1%, the new radius, r', can be expressed as:
- r' = r - 0.01r = 0.99r
New Speed Calculation
- The new speed v' becomes:
v' = √(GM/r')
- Substituting r' into the equation gives:
v' = √(GM/(0.99r))
Speed Comparison
- This simplifies to:
v' = √(GM/r) * √(1/0.99)
- Notably, since √(1/0.99) is greater than 1, we find that:
v' > v
Percentage Increase in Speed
- The percentage increase in speed can be calculated as:
(v' - v)/v * 100
- Since √(1/0.99) is approximately 1.005, the speed increases by roughly 0.5%.
Conclusion
The speed of the satellite increases by approximately 0.5% when the orbit radius is decreased by 1%. Thus, the correct option is:
Option: b) increases 0.5%
Community Answer
A satellite is moving round the earth with speed v in a circular orbit...
a
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A satellite is moving round the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1% then what is its speed. Option- a) increases 1%, b) increases 0.5%, c) decreases 1%, d) decreases 0.5%
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A satellite is moving round the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1% then what is its speed. Option- a) increases 1%, b) increases 0.5%, c) decreases 1%, d) decreases 0.5% for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A satellite is moving round the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1% then what is its speed. Option- a) increases 1%, b) increases 0.5%, c) decreases 1%, d) decreases 0.5% covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A satellite is moving round the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1% then what is its speed. Option- a) increases 1%, b) increases 0.5%, c) decreases 1%, d) decreases 0.5%.
A satellite is moving round the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1% then what is its speed. Option- a) increases 1%, b) increases 0.5%, c) decreases 1%, d) decreases 0.5% for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A satellite is moving round the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1% then what is its speed. Option- a) increases 1%, b) increases 0.5%, c) decreases 1%, d) decreases 0.5% covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A satellite is moving round the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1% then what is its speed. Option- a) increases 1%, b) increases 0.5%, c) decreases 1%, d) decreases 0.5%.
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