Q. A satellite is in a circular orbit around the Earth. If its orbital radius is 4R, what is the gravitational force acting on it compared to that at the surface of the Earth?
A.
1/4
B.
1/16
C.
1/8
D.
1/2
Solution
The gravitational force decreases with the square of the distance. At 4R, the force is 1/(4^2) = 1/16 of the force at the surface.
Q. A satellite is in a circular orbit around the Earth. If its speed is doubled, what will happen to its orbital radius?
A.
It will remain the same.
B.
It will double.
C.
It will increase by a factor of four.
D.
It will decrease by a factor of four.
Solution
If the speed of a satellite is doubled, the orbital radius will decrease by a factor of four, as orbital speed is inversely proportional to the square root of the radius.
Correct Answer:
D
— It will decrease by a factor of four.
Q. A satellite is in a circular orbit around the Earth. If its speed is doubled, what happens to the radius of its orbit?
A.
It remains the same
B.
It doubles
C.
It increases by a factor of four
D.
It decreases by a factor of four
Solution
If the speed of a satellite is doubled, the radius of its orbit decreases by a factor of four due to the relationship between speed and radius in circular motion.
Correct Answer:
D
— It decreases by a factor of four
Q. A satellite is in a circular orbit around the Earth. If the radius of the orbit is halved, what happens to the gravitational force acting on the satellite?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It decreases by half
Solution
The gravitational force is inversely proportional to the square of the distance; halving the radius increases the force by a factor of four.
Q. A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the gravitational acceleration is 9.8 m/s², what is the speed of the satellite?
Q. A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the speed of the satellite is 7.9 km/s, what is the centripetal acceleration?
Q. A satellite is in a circular orbit around the Earth. If the radius of the orbit is doubled, what happens to the gravitational force acting on the satellite?
A.
It doubles
B.
It halves
C.
It becomes four times
D.
It becomes one-fourth
Solution
Gravitational force ∝ 1/r². If radius is doubled, force becomes 1/(2²) = 1/4.
Q. A satellite is in a circular orbit around the Earth. What is the angular momentum of the satellite if its mass is m, its orbital radius is r, and its orbital speed is v?
A.
mv^2/r
B.
mvr
C.
mr^2
D.
mv
Solution
Angular momentum L = mvr, where v is the orbital speed and r is the radius of the orbit.
Q. A satellite is in a circular orbit around the Earth. What is the relationship between the gravitational force and the centripetal force acting on the satellite? (2022)
A.
Gravitational force > Centripetal force
B.
Gravitational force < Centripetal force
C.
Gravitational force = Centripetal force
D.
No relationship
Solution
For a satellite in a stable orbit, the gravitational force provides the necessary centripetal force, hence they are equal.
Correct Answer:
C
— Gravitational force = Centripetal force
Q. A scholarship fund awards $2000 to a student. If the fund increases the award by 15% each year, how much will the student receive after 2 years? (2022)
