Satellite Motion
Q. What happens to the gravitational force on a satellite as it moves further away from the Earth?
A.
It increases
B.
It decreases
C.
It remains constant
D.
It becomes zero
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Solution
The gravitational force on a satellite decreases as it moves further away from the Earth, following the inverse square law.
Correct Answer: B — It decreases
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Q. What happens to the gravitational force on a satellite as it moves to a higher orbit?
A.
It increases.
B.
It decreases.
C.
It remains constant.
D.
It becomes zero.
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Solution
The gravitational force on a satellite decreases as it moves to a higher orbit due to the inverse square law of gravitation.
Correct Answer: B — It decreases.
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Q. What happens to the gravitational force on a satellite if its altitude is doubled?
A.
It doubles
B.
It remains the same
C.
It becomes four times weaker
D.
It becomes eight times weaker
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Solution
The gravitational force decreases with the square of the distance from the center of the Earth. If the altitude is doubled, the distance from the center of the Earth becomes R + 2h, and the force becomes weaker by a factor of four.
Correct Answer: C — It becomes four times weaker
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Q. What happens to the gravitational potential energy of a satellite as it moves further away from the Earth?
A.
It increases
B.
It decreases
C.
It remains constant
D.
It becomes zero
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Solution
As a satellite moves further away from the Earth, its gravitational potential energy increases because it is moving to a higher potential.
Correct Answer: A — It increases
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Q. What happens to the gravitational potential energy of a satellite as it moves to a higher orbit?
A.
It increases
B.
It decreases
C.
It remains constant
D.
It becomes zero
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Solution
As a satellite moves to a higher orbit, its gravitational potential energy increases due to the increase in distance from the Earth.
Correct Answer: A — It increases
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Q. What is the effect of atmospheric drag on satellites in low Earth orbit?
A.
It increases their speed.
B.
It decreases their speed.
C.
It has no effect.
D.
It causes them to gain altitude.
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Solution
Atmospheric drag decreases the speed of satellites in low Earth orbit, leading to a gradual decrease in altitude.
Correct Answer: B — It decreases their speed.
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Q. What is the effect of increasing the altitude of a satellite on its orbital period?
A.
It decreases
B.
It increases
C.
It remains the same
D.
It becomes zero
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Solution
According to Kepler's third law, increasing the altitude of a satellite increases its orbital period.
Correct Answer: B — It increases
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Q. What is the effect of increasing the height of a satellite on its orbital speed?
A.
Increases speed
B.
Decreases speed
C.
No effect
D.
Doubles speed
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Solution
Increasing the height of a satellite decreases its orbital speed, as the gravitational force acting on it decreases.
Correct Answer: B — Decreases speed
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Q. What is the effect of increasing the mass of a satellite on its orbital radius if the orbital speed is to remain constant?
A.
The orbital radius must increase
B.
The orbital radius must decrease
C.
The orbital radius remains the same
D.
It has no effect on the orbital radius
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Solution
If the orbital speed is to remain constant, increasing the mass of the satellite requires an increase in the orbital radius due to the balance of gravitational and centripetal forces.
Correct Answer: A — The orbital radius must increase
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Q. What is the effect of increasing the mass of a satellite on its orbital radius?
A.
It increases the orbital radius.
B.
It decreases the orbital radius.
C.
It has no effect on the orbital radius.
D.
It depends on the altitude.
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Solution
The mass of the satellite does not affect its orbital radius; it is determined by the mass of the Earth and the orbital speed.
Correct Answer: C — It has no effect on the orbital radius.
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Q. What is the effect of increasing the mass of a satellite on its orbital speed?
A.
Increases the orbital speed
B.
Decreases the orbital speed
C.
No effect on orbital speed
D.
Depends on the altitude
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Solution
The orbital speed of a satellite depends on the mass of the Earth and the radius of the orbit, but not on the mass of the satellite itself. Therefore, increasing the mass of the satellite has no effect on its orbital speed.
Correct Answer: C — No effect on orbital speed
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Q. What is the escape velocity for a satellite to leave Earth's gravitational field?
A.
7.9 km/s
B.
11.2 km/s
C.
9.8 km/s
D.
5.0 km/s
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Solution
The escape velocity from the Earth's surface is approximately 11.2 km/s.
Correct Answer: B — 11.2 km/s
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Q. What is the escape velocity for a satellite to leave the Earth's gravitational field?
A.
7.9 km/s
B.
11.2 km/s
C.
9.8 km/s
D.
5.0 km/s
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Solution
The escape velocity from the Earth's surface is approximately 11.2 km/s.
Correct Answer: B — 11.2 km/s
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Q. What is the escape velocity for a satellite to leave the Earth's gravitational influence?
A.
11.2 km/s
B.
7.9 km/s
C.
9.8 km/s
D.
15.0 km/s
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Solution
The escape velocity from the Earth's surface is approximately 11.2 km/s.
Correct Answer: A — 11.2 km/s
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Q. What is the gravitational force acting on a satellite of mass m in orbit at a height h above the Earth's surface?
A.
GmM/(R+h)^2
B.
GmM/R^2
C.
GmM/(R-h)^2
D.
GmM/(R+h)
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Solution
The gravitational force acting on a satellite in orbit is given by F = GmM/(R+h)^2, where R is the radius of the Earth.
Correct Answer: A — GmM/(R+h)^2
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Q. What is the gravitational potential energy of a satellite of mass m at a height h above the Earth's surface?
A.
-GMm/R
B.
-GMm/(R+h)
C.
-GMm/(R-h)
D.
-GMm/(R^2 + h^2)
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Solution
The gravitational potential energy of a satellite at height h is given by U = -GMm/(R+h), where R is the radius of the Earth.
Correct Answer: B — -GMm/(R+h)
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Q. What is the minimum speed required for a satellite to achieve a low Earth orbit?
A.
7.9 km/s
B.
11.2 km/s
C.
5.0 km/s
D.
9.8 km/s
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Solution
The minimum speed required for a satellite to achieve a low Earth orbit is approximately 7.9 km/s.
Correct Answer: A — 7.9 km/s
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Q. What is the minimum speed required for a satellite to maintain a low Earth orbit?
A.
7.9 km/s
B.
11.2 km/s
C.
5.0 km/s
D.
9.8 km/s
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Solution
The minimum speed required for a satellite in low Earth orbit is approximately 7.9 km/s.
Correct Answer: A — 7.9 km/s
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Q. What is the orbital speed of a satellite in a circular orbit at a height h above the Earth's surface?
A.
sqrt(GM/R^2)
B.
sqrt(GM/(R+h)^2)
C.
sqrt(GM/(R-h)^2)
D.
sqrt(GM/R)
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Solution
The orbital speed v of a satellite in a circular orbit is given by v = sqrt(GM/(R+h)^2), where G is the gravitational constant, M is the mass of the Earth, R is the radius of the Earth, and h is the height of the satellite above the Earth's surface.
Correct Answer: B — sqrt(GM/(R+h)^2)
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Q. What is the orbital speed of a satellite in a low Earth orbit (LEO) approximately 2000 km above the Earth's surface? (2000)
A.
7.9 km/s
B.
11.2 km/s
C.
5.0 km/s
D.
3.0 km/s
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Solution
The orbital speed of a satellite in low Earth orbit is approximately 7.9 km/s.
Correct Answer: A — 7.9 km/s
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Q. What is the period of a satellite in a circular orbit at a height of 300 km above the Earth's surface?
A.
90 minutes
B.
60 minutes
C.
120 minutes
D.
30 minutes
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Solution
The period of a satellite in a circular orbit at a height of 300 km is approximately 90 minutes.
Correct Answer: A — 90 minutes
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Q. What is the period of a satellite in a low Earth orbit (LEO) compared to a satellite in a geostationary orbit?
A.
Longer than a geostationary orbit
B.
Shorter than a geostationary orbit
C.
Equal to a geostationary orbit
D.
Depends on the mass of the satellite
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Solution
Satellites in low Earth orbit have a much shorter orbital period compared to geostationary satellites due to their proximity to Earth.
Correct Answer: B — Shorter than a geostationary orbit
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Q. What is the primary force acting on a satellite in a stable orbit around the Earth?
A.
Gravitational force
B.
Electromagnetic force
C.
Frictional force
D.
Centrifugal force
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Solution
A satellite in a stable orbit is primarily influenced by the gravitational force exerted by the Earth.
Correct Answer: A — Gravitational force
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Q. What is the relationship between the height of a satellite and its orbital period?
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Exponential relationship
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Solution
The orbital period T of a satellite is related to its height h by T ∝ h^(3/2), which indicates that the period is inversely proportional to the square root of the gravitational force acting on it.
Correct Answer: B — Inversely proportional
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Q. What is the relationship between the orbital radius and the period of a satellite in a circular orbit?
A.
T is directly proportional to r
B.
T is inversely proportional to r
C.
T is proportional to r^2
D.
T is proportional to √r
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Solution
The period T of a satellite is proportional to the square root of the orbital radius r (T ∝ √r).
Correct Answer: D — T is proportional to √r
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Q. What is the relationship between the orbital radius and the time period of a satellite?
A.
T ∝ r^2
B.
T ∝ r^3/2
C.
T ∝ r
D.
T ∝ r^1/2
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Solution
The time period T of a satellite is related to the orbital radius r by T ∝ r^(3/2), according to Kepler's third law.
Correct Answer: B — T ∝ r^3/2
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Q. What is the relationship between the period of a satellite and its orbital radius?
A.
T is directly proportional to r
B.
T is inversely proportional to r
C.
T is proportional to r^2
D.
T is proportional to √r
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Solution
The period T of a satellite is proportional to the square root of the orbital radius r, as given by T = 2π√(r^3/GM).
Correct Answer: D — T is proportional to √r
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Q. What type of orbit does a satellite in a geosynchronous orbit have?
A.
Elliptical orbit
B.
Circular orbit
C.
Parabolic orbit
D.
Hyperbolic orbit
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Solution
A geosynchronous satellite typically has a circular orbit to maintain a constant position relative to the Earth's surface.
Correct Answer: B — Circular orbit
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Q. Which of the following factors does NOT affect the gravitational force acting on a satellite?
A.
Mass of the satellite
B.
Mass of the Earth
C.
Distance from the center of the Earth
D.
Speed of the satellite
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Solution
The gravitational force depends on the masses of the objects and the distance between them, but not on the speed of the satellite.
Correct Answer: D — Speed of the satellite
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Q. Which of the following factors does NOT affect the gravitational force between a satellite and the Earth?
A.
Mass of the satellite
B.
Mass of the Earth
C.
Distance between the satellite and the Earth
D.
Speed of the satellite
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Solution
The gravitational force depends on the masses and the distance, but not on the speed of the satellite.
Correct Answer: D — Speed of the satellite
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