Q. If the amplitude of a simple harmonic oscillator is tripled, how does the total energy change? (2020)
A.
Increases by 3 times
B.
Increases by 6 times
C.
Increases by 9 times
D.
Remains the same
Show solution
Solution
Total energy in SHM is proportional to the square of the amplitude. If amplitude is tripled, energy increases by 3^2 = 9 times.
Correct Answer:
C
— Increases by 9 times
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Q. If the amplitude of a wave is doubled, how does it affect the energy of the wave? (2020)
A.
Remains the same
B.
Doubles
C.
Increases by four times
D.
Halves
Show solution
Solution
Energy of a wave is proportional to the square of the amplitude. If amplitude is doubled, energy increases by (2^2) = 4 times.
Correct Answer:
C
— Increases by four times
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Q. If the amplitude of a wave is doubled, how does the energy of the wave change?
A.
Remains the same
B.
Doubles
C.
Increases by a factor of four
D.
Increases by a factor of eight
Show solution
Solution
The energy of a wave is proportional to the square of the amplitude. If the amplitude is doubled, the energy increases by a factor of 2^2 = 4.
Correct Answer:
C
— Increases by a factor of four
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Q. If the amplitude of a wave is doubled, how does this affect the energy carried by the wave? (2021)
A.
Energy is halved
B.
Energy remains the same
C.
Energy is doubled
D.
Energy is quadrupled
Show solution
Solution
The energy carried by a wave is proportional to the square of the amplitude. Therefore, if the amplitude is doubled, the energy increases by a factor of four.
Correct Answer:
D
— Energy is quadrupled
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Q. If the amplitude of a wave is doubled, what happens to its energy?
A.
Remains the same
B.
Doubles
C.
Increases by a factor of four
D.
Increases by a factor of eight
Show solution
Solution
The energy of a wave is proportional to the square of its amplitude. Therefore, if the amplitude is doubled, the energy increases by a factor of four.
Correct Answer:
C
— Increases by a factor of four
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Q. If the amplitude of a wave is increased, what effect does it have on the energy carried by the wave? (2019)
A.
Energy decreases
B.
Energy remains the same
C.
Energy increases
D.
Energy becomes zero
Show solution
Solution
The energy carried by a wave is proportional to the square of its amplitude. Therefore, if the amplitude increases, the energy also increases.
Correct Answer:
C
— Energy increases
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Q. If the amplitude of a wave is increased, what effect does it have on the energy of the wave? (2022)
A.
Energy decreases
B.
Energy remains the same
C.
Energy increases
D.
Energy becomes zero
Show solution
Solution
The energy of a wave is proportional to the square of its amplitude. Therefore, if the amplitude increases, the energy also increases.
Correct Answer:
C
— Energy increases
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Q. If the amplitude of a wave is increased, what happens to its energy? (2019)
A.
Decreases
B.
Increases
C.
Remains the same
D.
Becomes zero
Show solution
Solution
The energy of a wave is proportional to the square of its amplitude. Therefore, if the amplitude increases, the energy also increases.
Correct Answer:
B
— Increases
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Q. If the amplitude of a wave is tripled, how does the energy of the wave change?
A.
Increases by a factor of 3
B.
Increases by a factor of 6
C.
Increases by a factor of 9
D.
Remains the same
Show solution
Solution
Energy is proportional to the square of the amplitude, so if amplitude is tripled, energy increases by a factor of 3^2 = 9.
Correct Answer:
C
— Increases by a factor of 9
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Q. If the amplitude of a wave is tripled, what happens to its energy?
A.
Increases by a factor of 3
B.
Increases by a factor of 6
C.
Increases by a factor of 9
D.
Remains the same
Show solution
Solution
The energy of a wave is proportional to the square of its amplitude, so if amplitude is tripled, energy increases by a factor of 3^2 = 9.
Correct Answer:
C
— Increases by a factor of 9
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Q. If the amplitude of a wave is tripled, what happens to the energy carried by the wave? (2019)
A.
It remains the same
B.
It doubles
C.
It triples
D.
It increases by a factor of nine
Show solution
Solution
The energy carried by a wave is proportional to the square of the amplitude. Therefore, if the amplitude is tripled, the energy increases by a factor of 3^2 = 9.
Correct Answer:
D
— It increases by a factor of nine
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Q. If the angle between the current element and the line joining the current element to the point of interest is 90 degrees, what is the contribution of that current element to the magnetic field?
A.
Maximum
B.
Minimum
C.
Zero
D.
Undefined
Show solution
Solution
If the angle is 90 degrees, the sine of the angle is zero, resulting in zero contribution to the magnetic field from that current element.
Correct Answer:
C
— Zero
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Q. If the angle between the force and the lever arm is 90 degrees, how does it affect the torque?
A.
Torque is zero
B.
Torque is maximum
C.
Torque is half
D.
Torque is minimum
Show solution
Solution
Torque is maximum when the angle is 90 degrees because τ = F × r × sin(θ) and sin(90°) = 1.
Correct Answer:
B
— Torque is maximum
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Q. If the angle between the force and the lever arm is 90 degrees, what is the torque produced by a 15 N force applied at a distance of 2 m?
A.
0 Nm
B.
15 Nm
C.
30 Nm
D.
45 Nm
Show solution
Solution
Torque (τ) = F × d × sin(θ) = 15 N × 2 m × sin(90°) = 30 Nm.
Correct Answer:
C
— 30 Nm
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Q. If the angle between the transmission axis of two polarizers is 90 degrees, what is the intensity of light passing through them?
A.
Maximum intensity
B.
Half of the original intensity
C.
Zero intensity
D.
Equal to the intensity of the first polarizer
Show solution
Solution
When the angle between the transmission axes of two polarizers is 90 degrees, no light passes through, resulting in zero intensity.
Correct Answer:
C
— Zero intensity
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Q. If the angle between the transmission axis of two polarizers is 90 degrees, what is the transmitted intensity of light?
A.
Maximum intensity
B.
Half of the original intensity
C.
Zero intensity
D.
One-fourth of the original intensity
Show solution
Solution
When the angle between the transmission axes of two polarizers is 90 degrees, no light is transmitted, resulting in zero intensity.
Correct Answer:
C
— Zero intensity
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Q. If the angle between two vectors A and B is 60 degrees and |A| = 5, |B| = 10, what is the scalar product A · B? (2020)
Show solution
Solution
A · B = |A||B|cos(60°) = 5 * 10 * 0.5 = 25
Correct Answer:
B
— 30
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Q. If the angle between two vectors A and B is 60 degrees and |A| = 5, |B| = 10, what is A · B?
Show solution
Solution
A · B = |A||B|cos(60°) = 5 * 10 * 0.5 = 25.
Correct Answer:
B
— 30
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Q. If the angle between two vectors A and B is 90 degrees, what is A · B?
Show solution
Solution
A · B = |A||B|cos(90°) = |A||B| * 0 = 0.
Correct Answer:
A
— 0
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Q. If the angle between two vectors A and B is 90 degrees, what is the value of A · B?
A.
1
B.
0
C.
undefined
D.
1/2
Show solution
Solution
If the angle is 90 degrees, A · B = |A||B|cos(90) = 0.
Correct Answer:
B
— 0
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Q. If the angle between vectors A = 2i + 3j and B = 4i + 5j is 60 degrees, find A · B.
Show solution
Solution
A · B = |A||B|cos(60°) = √(2^2 + 3^2) * √(4^2 + 5^2) * 1/2 = √13 * √41 * 1/2 = 20.
Correct Answer:
B
— 25
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Q. If the angle of elevation from a point 30 meters away from the base of a hill is 60 degrees, what is the height of the hill?
A.
15√3 meters
B.
30 meters
C.
20 meters
D.
10√3 meters
Show solution
Solution
Using the tangent function, tan(60) = height / 30. Therefore, height = 30 * tan(60) = 30 * √3 = 30√3 meters.
Correct Answer:
A
— 15√3 meters
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Q. If the angle of elevation from a point 50 meters away from the base of a tower is 30 degrees, what is the height of the tower?
A.
25 meters
B.
50 meters
C.
10√3 meters
D.
15 meters
Show solution
Solution
Let h be the height of the tower. tan(30°) = h/50. Therefore, h = 50 * tan(30°) = 50 * (1/√3) = 50/√3 = 25√3/3 meters.
Correct Answer:
A
— 25 meters
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Q. If the angle of elevation of a hill from a point on the ground is 30 degrees and the distance from the point to the base of the hill is 100 m, what is the height of the hill? (2021)
A.
50 m
B.
30 m
C.
20 m
D.
10 m
Show solution
Solution
Height = distance * tan(30) = 100 * (1/√3) ≈ 57.74 m, which rounds to 50 m.
Correct Answer:
A
— 50 m
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Q. If the angle of elevation of the sun is 30 degrees, how tall is a 10 m pole casting a shadow? (2023)
A.
5 m
B.
10 m
C.
15 m
D.
20 m
Show solution
Solution
Height = shadow * tan(angle) = 10 * tan(30) = 10 * (1/√3) ≈ 10 m.
Correct Answer:
B
— 10 m
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Q. If the angle of elevation of the sun is 30 degrees, how tall is a 10 meter pole casting a shadow?
A.
5√3 m
B.
10 m
C.
10√3 m
D.
5 m
Show solution
Solution
Height = shadow * tan(angle) = 10 * √3 = 5√3 m.
Correct Answer:
A
— 5√3 m
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Q. If the angle of elevation of the sun is 30 degrees, how tall is a 10-meter pole casting a shadow of 10√3 meters? (2023)
A.
5 m
B.
10 m
C.
15 m
D.
20 m
Show solution
Solution
Height = Shadow * tan(30) = 10√3 * (1/√3) = 10 m.
Correct Answer:
B
— 10 m
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Q. If the angle of incidence in a medium is 45° and the refractive index of the medium is 1.5, what is the angle of refraction in air?
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
Using Snell's law: n1 * sin(θ1) = n2 * sin(θ2), 1.5 * sin(45°) = 1 * sin(θ2) => sin(θ2) = 1.5 * 0.7071 = 1.0607, which is not possible, hence total internal reflection occurs.
Correct Answer:
C
— 60°
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Q. If the angle of incidence in a medium is 70° and the refractive index of the medium is 1.5, will total internal reflection occur?
A.
Yes
B.
No
C.
Only at certain angles
D.
Not applicable
Show solution
Solution
Since 70° > θc = sin⁻¹(1/1.5) ≈ 41.8°, total internal reflection will occur.
Correct Answer:
A
— Yes
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Q. If the angle of incidence in glass (n=1.5) is 60°, will total internal reflection occur when light travels to air?
A.
Yes
B.
No
C.
Depends on the angle
D.
Not enough information
Show solution
Solution
Since the critical angle for glass to air is sin⁻¹(1.00/1.5) ≈ 41.8°, and 60° > 41.8°, total internal reflection occurs.
Correct Answer:
A
— Yes
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