Q. A pendulum swings with a period of 1 second. If the length of the pendulum is increased by a factor of 4, what will be the new period?
A.
1 s
B.
2 s
C.
4 s
D.
√4 s
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Solution
The period T = 2π√(L/g). If L is increased by a factor of 4, T increases by a factor of √4 = 2.
Correct Answer: B — 2 s
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Q. A pendulum swings with a period of 1 second. If the length of the pendulum is tripled, what will be the new period?
A.
1 s
B.
2 s
C.
3 s
D.
√3 s
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Solution
The period T = 2π√(L/g). If L is tripled, T becomes √3 times longer, so T = 2 s.
Correct Answer: B — 2 s
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Q. A pendulum swings with a period of 1 second. What is the length of the pendulum?
A.
0.25 m
B.
0.5 m
C.
1 m
D.
2 m
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Solution
Length L = (gT^2)/(4π^2) = (9.8 * 1^2)/(4 * π^2) ≈ 1 m.
Correct Answer: C — 1 m
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Q. A pendulum swings with a period of 1.5 seconds. What is the angular frequency of the pendulum?
A.
2π/1.5 rad/s
B.
4π/3 rad/s
C.
π/1.5 rad/s
D.
3π/2 rad/s
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Solution
Angular frequency (ω) = 2π/T = 2π/1.5 = 4π/3 rad/s.
Correct Answer: B — 4π/3 rad/s
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Q. A pendulum swings with a period of 2 seconds. What is the frequency of the pendulum?
A.
0.25 Hz
B.
0.5 Hz
C.
1 Hz
D.
2 Hz
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Solution
Frequency (f) is the reciprocal of the period (T). Therefore, f = 1/T = 1/2 = 0.5 Hz.
Correct Answer: B — 0.5 Hz
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Q. A pendulum swings with a period of 2 seconds. What is the length of the pendulum?
A.
0.5 m
B.
1 m
C.
2 m
D.
4 m
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Solution
The period T of a simple pendulum is given by T = 2π√(L/g). Rearranging gives L = (T²g)/(4π²). Using g = 9.8 m/s², L = (2² * 9.8)/(4π²) ≈ 1 m.
Correct Answer: B — 1 m
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Q. A pendulum swings with a period T. What is the period of a pendulum of length 4L?
A.
2T
B.
T/2
C.
T√2
D.
2√2T
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Solution
The period T of a simple pendulum is given by T = 2π√(L/g). For length 4L, T' = 2π√(4L/g) = 2T.
Correct Answer: A — 2T
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Q. A pendulum swings with a small amplitude. The restoring force acting on the pendulum is proportional to which of the following?
A.
Displacement from equilibrium
B.
Velocity
C.
Acceleration
D.
Mass
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Solution
In simple harmonic motion, the restoring force is proportional to the displacement from the equilibrium position.
Correct Answer: A — Displacement from equilibrium
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Q. A pendulum swings with a small amplitude. What type of motion does it exhibit?
A.
Linear motion
B.
Rotational motion
C.
Simple harmonic motion
D.
Circular motion
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Solution
A pendulum swinging with a small amplitude exhibits simple harmonic motion.
Correct Answer: C — Simple harmonic motion
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Q. A pendulum's period is measured as 2.0 s with an uncertainty of ±0.1 s. What is the relative uncertainty?
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Solution
Relative uncertainty = (Uncertainty / Measured value) * 100 = (0.1 / 2.0) * 100 = 5%.
Correct Answer: A — 5%
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Q. A pendulum's period is measured as 2.0 s with an uncertainty of ±0.1 s. What is the fractional error in the period?
A.
0.05
B.
0.1
C.
0.02
D.
0.1
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Solution
Fractional error = (absolute error / measured value) = 0.1 / 2.0 = 0.05.
Correct Answer: A — 0.05
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Q. A pendulum's period is measured as 2.0 s with an uncertainty of ±0.1 s. What is the percentage uncertainty in the measurement?
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Solution
Percentage uncertainty = (Uncertainty / Measured value) * 100 = (0.1 / 2.0) * 100 = 5%.
Correct Answer: A — 5%
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Q. A person is pushing a heavy box across a floor. If the box does not move, what can be said about the forces acting on it?
A.
Net force is zero
B.
Net force is positive
C.
Net force is negative
D.
Only friction is acting
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Solution
If the box does not move, the net force acting on it is zero, meaning the applied force equals the frictional force.
Correct Answer: A — Net force is zero
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Q. A person is running at 3 m/s on a moving escalator that moves at 2 m/s in the same direction. What is the speed of the person relative to a stationary observer?
A.
1 m/s
B.
3 m/s
C.
5 m/s
D.
2 m/s
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Solution
Speed of person relative to observer = Speed of escalator + Speed of person = 2 m/s + 3 m/s = 5 m/s.
Correct Answer: C — 5 m/s
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Q. A person is running at 8 m/s in a train moving at 12 m/s in the same direction. What is the speed of the person relative to the ground?
A.
4 m/s
B.
8 m/s
C.
12 m/s
D.
20 m/s
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Solution
Speed of person relative to ground = Speed of train + Speed of person = 12 m/s + 8 m/s = 20 m/s.
Correct Answer: D — 20 m/s
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Q. A person is running at 8 m/s on a moving walkway that moves at 2 m/s in the same direction. What is the speed of the person relative to the ground?
A.
6 m/s
B.
8 m/s
C.
10 m/s
D.
12 m/s
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Solution
Speed relative to ground = Speed of person + Speed of walkway = 8 m/s + 2 m/s = 10 m/s.
Correct Answer: C — 10 m/s
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Q. A person is running at a speed of 10 m/s. If he is running towards a train moving at 20 m/s in the opposite direction, what is the relative speed of the train with respect to the person?
A.
10 m/s
B.
20 m/s
C.
30 m/s
D.
40 m/s
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Solution
Relative speed = speed of train + speed of person = 20 + 10 = 30 m/s.
Correct Answer: C — 30 m/s
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Q. A person is walking at 2 m/s on a train moving at 10 m/s. What is the speed of the person relative to the ground?
A.
2 m/s
B.
8 m/s
C.
10 m/s
D.
12 m/s
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Solution
Speed of person relative to ground = Speed of train + Speed of person = 10 m/s + 2 m/s = 12 m/s.
Correct Answer: D — 12 m/s
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Q. A person is walking at 4 km/h in a train moving at 36 km/h. What is the speed of the person relative to the ground?
A.
32 km/h
B.
40 km/h
C.
36 km/h
D.
4 km/h
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Solution
Speed of person relative to ground = Speed of train + Speed of person = 36 km/h + 4 km/h = 40 km/h.
Correct Answer: B — 40 km/h
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Q. A person lifts a box of mass 10 kg to a height of 2 m in 4 seconds. What is the power exerted by the person?
A.
50 W
B.
25 W
C.
100 W
D.
75 W
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Solution
The work done against gravity is W = mgh = 10 kg * 9.8 m/s² * 2 m = 196 J. Power is P = W/t = 196 J / 4 s = 49 W, approximately 50 W.
Correct Answer: A — 50 W
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Q. A person pushes a box with a force of 30 N, but the box does not move. If the coefficient of static friction is 0.6, what is the maximum static friction force?
A.
18 N
B.
30 N
C.
36 N
D.
60 N
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Solution
The maximum static friction force is equal to the applied force when the box does not move, which is 30 N.
Correct Answer: C — 36 N
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Q. A person walks at 4 km/h and runs at 10 km/h. If he walks for 30 minutes and then runs for 1 hour, how far does he travel?
A.
7 km
B.
8 km
C.
9 km
D.
10 km
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Solution
Distance walked = 4 * 0.5 = 2 km; Distance run = 10 * 1 = 10 km; Total distance = 2 + 10 = 12 km.
Correct Answer: C — 9 km
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Q. A person walks at 4 km/h and runs at 10 km/h. If he walks for 30 minutes and then runs for 30 minutes, how far does he travel?
A.
5 km
B.
7 km
C.
8 km
D.
10 km
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Solution
Distance walked = 4 km/h * 0.5 h = 2 km. Distance run = 10 km/h * 0.5 h = 5 km. Total distance = 2 + 5 = 7 km.
Correct Answer: C — 8 km
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Q. A person walks at 4 km/h and runs at 10 km/h. If he walks for 30 minutes and then runs for 30 minutes, what is his average speed?
A.
6 km/h
B.
7 km/h
C.
8 km/h
D.
9 km/h
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Solution
Total distance = (4 × 0.5) + (10 × 0.5) = 2 + 5 = 7 km. Total time = 1 hour. Average speed = 7 km/h.
Correct Answer: B — 7 km/h
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Q. A person walks at 4 km/h in a train moving at 36 km/h. What is the speed of the person relative to the ground?
A.
32 km/h
B.
36 km/h
C.
40 km/h
D.
4 km/h
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Solution
Speed of person relative to ground = Speed of train + Speed of person = 36 km/h + 4 km/h = 40 km/h.
Correct Answer: C — 40 km/h
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Q. A person walks at 4 km/h in a train moving at 60 km/h. What is the speed of the person relative to the ground?
A.
64 km/h
B.
60 km/h
C.
4 km/h
D.
56 km/h
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Solution
Speed of person relative to ground = Speed of train + Speed of person = 60 km/h + 4 km/h = 64 km/h.
Correct Answer: A — 64 km/h
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Q. A person walks at 4 km/h in still water. If the current of the river is 2 km/h, what is the speed of the person relative to the bank when walking upstream?
A.
2 km/h
B.
4 km/h
C.
6 km/h
D.
8 km/h
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Solution
Speed upstream = Speed of person - Speed of current = 4 km/h - 2 km/h = 2 km/h.
Correct Answer: A — 2 km/h
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Q. A person walks at 4 km/h on a moving escalator that moves at 2 km/h. What is the speed of the person relative to a stationary observer?
A.
2 km/h
B.
4 km/h
C.
6 km/h
D.
8 km/h
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Solution
Speed of person relative to observer = Speed of person + Speed of escalator = 4 km/h + 2 km/h = 6 km/h.
Correct Answer: C — 6 km/h
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Q. A physical quantity is measured as 50.0 units with an uncertainty of ±1.0 units. If this quantity is multiplied by 3, what is the new uncertainty?
A.
3.0 units
B.
1.0 units
C.
2.0 units
D.
4.0 units
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Solution
New uncertainty = 3 * (uncertainty) = 3 * 1.0 = 3.0 units.
Correct Answer: A — 3.0 units
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Q. A plane flies 300 km north and then 400 km east. What is the angle of the resultant displacement with respect to the north?
A.
36.87 degrees
B.
45 degrees
C.
53.13 degrees
D.
60 degrees
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Solution
Angle = tan^(-1)(400/300) = 53.13 degrees.
Correct Answer: C — 53.13 degrees
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