Q. A rotating object has a moment of inertia of 3 kg·m² and is spinning with an angular velocity of 4 rad/s. What is its kinetic energy? (2023)
A.
12 J
B.
24 J
C.
48 J
D.
6 J
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Solution
The rotational kinetic energy is given by KE = 0.5 I ω² = 0.5 * 3 * (4)² = 24 J.
Correct Answer: B — 24 J
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Q. A rotating object has a moment of inertia of 5 kg·m² and is rotating with an angular velocity of 4 rad/s. What is its kinetic energy? (2022)
A.
40 J
B.
20 J
C.
10 J
D.
80 J
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Solution
The rotational kinetic energy is given by KE = (1/2)Iω² = (1/2)(5 kg·m²)(4 rad/s)² = 40 J.
Correct Answer: A — 40 J
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Q. A rotating object has an angular momentum L. If its moment of inertia is halved and angular velocity is doubled, what is the new angular momentum? (2022)
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Solution
L = Iω, if I is halved and ω is doubled, L' = (1/2)(2ω) = L.
Correct Answer: B — 2L
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Q. A rotating object has an angular momentum L. If the moment of inertia of the object is doubled while keeping the angular velocity constant, what happens to the angular momentum?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Angular momentum L = Iω. If I is doubled and ω remains constant, L also doubles.
Correct Answer: A — It doubles
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Q. A rotating object has an angular momentum of 10 kg·m²/s and a moment of inertia of 2 kg·m². What is its angular velocity?
A.
5 rad/s
B.
2 rad/s
C.
10 rad/s
D.
20 rad/s
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Solution
Using L = Iω, we find ω = L/I = 10/2 = 5 rad/s.
Correct Answer: A — 5 rad/s
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Q. A rotating object has an angular momentum of 10 kg·m²/s. If its moment of inertia is 2 kg·m², what is its angular velocity?
A.
5 rad/s
B.
2 rad/s
C.
10 rad/s
D.
20 rad/s
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Solution
Using L = Iω, we have ω = L/I = 10 kg·m²/s / 2 kg·m² = 5 rad/s.
Correct Answer: A — 5 rad/s
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Q. A rotating object has an angular momentum of 12 kg·m²/s and a moment of inertia of 4 kg·m². What is its angular velocity?
A.
3 rad/s
B.
4 rad/s
C.
2 rad/s
D.
1 rad/s
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Solution
Angular momentum L = Iω, thus ω = L/I = 12 kg·m²/s / 4 kg·m² = 3 rad/s.
Correct Answer: A — 3 rad/s
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Q. A rotating object has an angular momentum of 15 kg·m²/s. If its moment of inertia is 3 kg·m², what is its angular velocity?
A.
5 rad/s
B.
10 rad/s
C.
15 rad/s
D.
20 rad/s
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Solution
Angular momentum L = Iω, thus ω = L/I = 15 kg·m²/s / 3 kg·m² = 5 rad/s.
Correct Answer: B — 10 rad/s
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Q. A rotating object has an angular momentum of L. If its angular velocity is doubled and its moment of inertia remains constant, what will be the new angular momentum?
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Solution
Angular momentum L = Iω, if ω is doubled, L becomes 2I(2ω) = 4L.
Correct Answer: C — 4L
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Q. A rotating object has an angular momentum of L. If its moment of inertia is doubled while keeping the angular velocity constant, what will happen to its angular momentum?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It becomes zero
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Solution
Angular momentum L = Iω; if I is doubled and ω remains constant, L remains the same.
Correct Answer: C — It remains the same
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Q. A rotating object has an angular momentum of L. If its moment of inertia is halved and the angular velocity is doubled, what is the new angular momentum?
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Solution
New angular momentum L' = I'ω' = (1/2 I)(2ω) = Iω = L.
Correct Answer: C — 4L
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Q. A rotating object has an angular momentum of L. If its moment of inertia is halved and its angular velocity is doubled, what is the new angular momentum?
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Solution
New angular momentum L' = I'ω' = (1/2I)(2ω) = L.
Correct Answer: C — 4L
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Q. A rotating object has an angular velocity of 30 rad/s and a moment of inertia of 3 kg·m². What is its rotational kinetic energy?
A.
135 J
B.
450 J
C.
270 J
D.
90 J
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Solution
Rotational kinetic energy K = (1/2)Iω² = (1/2)(3 kg·m²)(30 rad/s)² = 450 J.
Correct Answer: B — 450 J
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Q. A rotating object has an angular velocity of 30 rad/s. If it is brought to rest in 5 seconds, what is the angular deceleration?
A.
6 rad/s²
B.
5 rad/s²
C.
3 rad/s²
D.
4 rad/s²
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Solution
Angular deceleration = (final angular velocity - initial angular velocity) / time = (0 - 30 rad/s) / 5 s = -6 rad/s².
Correct Answer: A — 6 rad/s²
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Q. A rotating system has an initial angular momentum L. If no external torque acts on it, what will be the angular momentum after some time?
A.
L
B.
0
C.
Increases
D.
Decreases
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Solution
Angular momentum is conserved in the absence of external torque.
Correct Answer: A — L
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Q. A rotating wheel has an angular momentum of 10 kg·m²/s. If its moment of inertia is 2 kg·m², what is its angular velocity?
A.
5 rad/s
B.
10 rad/s
C.
20 rad/s
D.
2 rad/s
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Solution
Using L = Iω, we have ω = L/I = 10/2 = 5 rad/s.
Correct Answer: A — 5 rad/s
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Q. A rotating wheel has an angular momentum of L. If its angular velocity is doubled, what will be the new angular momentum?
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Solution
Angular momentum L = Iω, if ω is doubled, L becomes 2I(2ω) = 4L.
Correct Answer: C — 4L
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Q. A rotating wheel has an angular momentum of L. If the wheel's angular velocity is doubled, what happens to its angular momentum?
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Solution
Angular momentum L = Iω; if ω is doubled, L becomes 2I(2ω) = 4L.
Correct Answer: C — 4L
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Q. A rotating wheel has an angular momentum of L. If the wheel's angular velocity is doubled, what will be the new angular momentum?
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Solution
Angular momentum L is proportional to angular velocity, so if angular velocity is doubled, angular momentum becomes 4L.
Correct Answer: C — 4L
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Q. A runner completes a 400 m lap in 50 seconds. What is his average velocity?
A.
6 m/s
B.
7 m/s
C.
8 m/s
D.
9 m/s
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Solution
Average velocity = total distance / total time = 400 m / 50 s = 8 m/s.
Correct Answer: A — 6 m/s
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Q. A runner completes a 400 m lap in 50 seconds. What is the average speed of the runner in m/s? (2019)
A.
6 m/s
B.
7 m/s
C.
8 m/s
D.
9 m/s
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Solution
Average speed = Total distance / Total time = 400 m / 50 s = 8 m/s.
Correct Answer: A — 6 m/s
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Q. A runner completes a 400 m lap in 50 seconds. What is the average velocity of the runner?
A.
8 m/s
B.
6 m/s
C.
4 m/s
D.
2 m/s
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Solution
Average velocity = total displacement / total time. Since the runner returns to the starting point, displacement = 0. Average velocity = 0 m / 50 s = 0 m/s.
Correct Answer: B — 6 m/s
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Q. A runner completes a 400 m lap in 50 seconds. What is the runner's average velocity?
A.
8 m/s
B.
6 m/s
C.
4 m/s
D.
2 m/s
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Solution
Average velocity = total displacement / total time. Since the runner returns to the starting point, displacement = 0. Average velocity = 0 m/s.
Correct Answer: A — 8 m/s
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Q. A runner completes a 400 m track in 50 seconds. What is their speed in m/s? (2023)
A.
6 m/s
B.
7 m/s
C.
8 m/s
D.
9 m/s
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Solution
Speed = Distance/Time = 400 m/50 s = 8 m/s
Correct Answer: A — 6 m/s
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Q. A runner completes a 5 km race in 25 minutes. What is his speed in km/h? (2023)
A.
10 km/h
B.
12 km/h
C.
14 km/h
D.
15 km/h
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Solution
Speed = Distance / Time = 5 km / (25/60) hours = 5 / (5/12) = 12 km/h.
Correct Answer: A — 10 km/h
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Q. A satellite is in a circular orbit around the Earth. How does the gravitational potential energy change 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 the satellite moves to a higher orbit, its gravitational potential energy increases.
Correct Answer: A — It increases.
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Q. A satellite is in a circular orbit around the Earth. If it moves to a higher orbit, what happens to its potential energy?
A.
It increases.
B.
It decreases.
C.
It remains constant.
D.
It becomes zero.
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Solution
As the satellite moves to a higher orbit, its gravitational potential energy increases due to the increase in distance from the Earth's center.
Correct Answer: A — It increases.
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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
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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.
Correct Answer: B — 1/16
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Q. A satellite is in a circular orbit around the Earth. If its orbital radius is tripled, how does the orbital speed change?
A.
It triples
B.
It doubles
C.
It remains the same
D.
It is reduced to one-third
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Solution
Orbital speed v = √(GM/R). If R is tripled, v becomes √(GM/(3R)) = v/√3, which is reduced to one-third.
Correct Answer: D — It is reduced to one-third
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Q. A satellite is in a circular orbit around the Earth. If its orbital radius is tripled, how does the gravitational force acting on it change?
A.
It triples
B.
It halves
C.
It becomes one-ninth
D.
It remains the same
Show solution
Solution
Gravitational force is inversely proportional to the square of the radius. If radius is tripled, force becomes 1/3² = 1/9.
Correct Answer: C — It becomes one-ninth
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