Q. If the amount after 2 years at compound interest is Rs. 1210 and the principal is Rs. 1000, what is the rate of interest?
A.
10%
B.
5%
C.
12%
D.
15%
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Solution
Using the formula A = P(1 + r)^t, we have 1210 = 1000(1 + r)^2. Solving gives r = 0.1 or 10%.
Correct Answer: A — 10%
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Q. If the amplitude of a damped oscillator decreases to half its value in 5 seconds, what is the damping ratio?
A.
0.1
B.
0.2
C.
0.3
D.
0.4
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Solution
Using the formula A(t) = A_0 e^(-ζω_nt), we find ζ = 0.2.
Correct Answer: B — 0.2
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Q. If the amplitude of a simple harmonic motion is doubled, how does the maximum velocity change?
A.
It doubles
B.
It quadruples
C.
It remains the same
D.
It halves
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Solution
Maximum velocity V_max = Aω. If A is doubled, V_max also doubles.
Correct Answer: A — It doubles
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Q. If the amplitude of a simple harmonic motion is doubled, how does the total energy change?
A.
Remains the same
B.
Doubles
C.
Quadruples
D.
Halves
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Solution
The total energy E in SHM is given by E = (1/2)kA². If A is doubled, E becomes (1/2)k(2A)² = 4(1/2)kA², which is quadrupled.
Correct Answer: C — Quadruples
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Q. If the amplitude of a simple harmonic motion is doubled, what happens to the total energy of the system? (2022)
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It halves
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Solution
Total energy (E) in SHM is proportional to the square of the amplitude (A). If A is doubled, E becomes 4A^2, hence it quadruples.
Correct Answer: C — It quadruples
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Q. If the amplitude of a simple harmonic motion is halved, how does the maximum velocity change?
A.
Halved
B.
Doubled
C.
Remains the same
D.
Quadrupled
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Solution
Maximum velocity V_max = ωA. If A is halved, V_max is also halved.
Correct Answer: A — Halved
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Q. If the amplitude of a simple harmonic oscillator is doubled, how does the total energy change?
A.
Remains the same
B.
Doubles
C.
Quadruples
D.
Halves
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Solution
The total energy in simple harmonic motion is proportional to the square of the amplitude. If amplitude is doubled, energy increases by a factor of 2^2 = 4.
Correct Answer: C — Quadruples
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Q. If the amplitude of a simple harmonic oscillator is doubled, what happens to its total energy?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It halves
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Solution
The total energy of a simple harmonic oscillator 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 — It quadruples
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Q. If the amplitude of a simple harmonic oscillator is halved, how does the total energy change?
A.
Remains the same
B.
Halved
C.
Doubled
D.
Quadrupled
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Solution
The total energy in SHM is proportional to the square of the amplitude. If amplitude is halved, energy is reduced to (1/2)^2 = 1/4, which is halved.
Correct Answer: B — Halved
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Q. If the amplitude of a simple harmonic oscillator is increased, what happens to its total energy? (2021)
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
The total energy (E) in a simple harmonic oscillator is given by E = (1/2)kA². If amplitude (A) increases, energy increases.
Correct Answer: A — Increases
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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
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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
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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
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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 of the wave? (2022)
A.
Energy decreases
B.
Energy remains the same
C.
Energy increases
D.
Energy becomes zero
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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 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
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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 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
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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
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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
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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 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 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 two vectors A and B is 60 degrees and |A| = 5, |B| = 10, what is A · B?
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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 the scalar product A · B? (2020)
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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 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.
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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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