Q. A wave on a string is described by the equation y(x, t) = 0.1 sin(2π(0.5x - 10t)). What is the speed of the wave?
A.
5 m/s
B.
10 m/s
C.
20 m/s
D.
25 m/s
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Solution
The speed of the wave v is given by v = fλ. Here, f = 10 Hz and λ = 2 m (from k = 2π/λ). Thus, v = 10 * 2 = 20 m/s.
Correct Answer: B — 10 m/s
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Q. A wave on a string is described by the equation y(x, t) = 0.1 sin(2π(0.5x - 2t)). What is the speed of the wave?
A.
1 m/s
B.
2 m/s
C.
0.5 m/s
D.
4 m/s
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Solution
The speed of the wave v is given by v = ω/k. Here, ω = 2π(2) = 4π rad/s and k = 2π(0.5) = π rad/m. Thus, v = (4π)/(π) = 4 m/s.
Correct Answer: B — 2 m/s
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Q. A wave on a string is described by the equation y(x, t) = 0.1 sin(2πx - 4πt). What is the amplitude of the wave?
A.
0.1 m
B.
0.2 m
C.
0.4 m
D.
1 m
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Solution
The amplitude is the coefficient of the sine function, which is 0.1 m.
Correct Answer: A — 0.1 m
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Q. A wave on a string is described by the equation y(x, t) = A sin(kx - ωt). What does 'A' represent?
A.
Wavelength
B.
Frequency
C.
Amplitude
D.
Wave number
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Solution
'A' represents the amplitude of the wave, which is the maximum displacement from the equilibrium position.
Correct Answer: C — Amplitude
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Q. A wave on a string is described by the equation y(x, t) = A sin(kx - ωt). What does 'k' represent?
A.
Angular frequency
B.
Wave number
C.
Amplitude
D.
Phase constant
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Solution
'k' is the wave number, which is related to the wavelength of the wave.
Correct Answer: B — Wave number
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Q. A wave traveling along a string is described by the equation y(x, t) = 0.1 sin(2π(0.5x - 2t)). What is the speed of the wave?
A.
1 m/s
B.
2 m/s
C.
3 m/s
D.
4 m/s
Show solution
Solution
The speed of the wave v is given by v = fλ. Here, f = 2 Hz and λ = 1 m (from the wave equation). Thus, v = 2 * 1 = 2 m/s.
Correct Answer: B — 2 m/s
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Q. A wave traveling along a string is described by the equation y(x, t) = 0.1 sin(2π(0.5x - 4t)). What is the wave speed?
A.
2 m/s
B.
4 m/s
C.
8 m/s
D.
1 m/s
Show solution
Solution
The wave speed v can be found from the equation v = fλ. Here, f = 4 Hz and λ = 2 m (from k = 2π/λ, k = 1 m⁻¹). Thus, v = 4 Hz * 2 m = 8 m/s.
Correct Answer: B — 4 m/s
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Q. A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). If A = 2 m, k = 3 rad/m, and ω = 6 rad/s, what is the amplitude of the wave?
A.
1 m
B.
2 m
C.
3 m
D.
4 m
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Solution
The amplitude of the wave is given directly by A in the wave equation. Here, A = 2 m.
Correct Answer: B — 2 m
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Q. A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). What does 'A' represent?
A.
Wavelength
B.
Amplitude
C.
Frequency
D.
Speed
Show solution
Solution
'A' represents the amplitude of the wave, which is the maximum displacement from the equilibrium position.
Correct Answer: B — Amplitude
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Q. A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). What does 'k' represent?
A.
Amplitude
B.
Wave number
C.
Frequency
D.
Angular frequency
Show solution
Solution
'k' is the wave number, which is related to the wavelength λ by the equation k = 2π/λ.
Correct Answer: B — Wave number
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Q. A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). What is the phase velocity of the wave?
A.
A/k
B.
ω/k
C.
k/ω
D.
Aω
Show solution
Solution
The phase velocity v is given by v = ω/k.
Correct Answer: B — ω/k
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Q. A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). What does the parameter A represent?
A.
Wavelength
B.
Amplitude
C.
Frequency
D.
Speed
Show solution
Solution
In the wave equation y(x, t) = A sin(kx - ωt), A represents the amplitude of the wave, which is the maximum displacement from the equilibrium position.
Correct Answer: B — Amplitude
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Q. A wave travels along a string with a speed of 300 m/s and has a frequency of 150 Hz. What is the wavelength of the wave?
A.
1.0 m
B.
2.0 m
C.
3.0 m
D.
4.0 m
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Solution
Wavelength λ is given by λ = v/f. Here, v = 300 m/s and f = 150 Hz. Thus, λ = 300/150 = 2.0 m.
Correct Answer: B — 2.0 m
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Q. A wave travels at a speed of 300 m/s and has a frequency of 150 Hz. What is its wavelength?
A.
2 m
B.
1.5 m
C.
3 m
D.
0.5 m
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Solution
The wavelength λ can be calculated using the formula v = fλ. Thus, λ = v/f = 300 m/s / 150 Hz = 2 m.
Correct Answer: B — 1.5 m
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Q. A wave travels through a medium with a frequency of 500 Hz and a wavelength of 2 m. What is the speed of the wave?
A.
1000 m/s
B.
250 m/s
C.
500 m/s
D.
2000 m/s
Show solution
Solution
The speed of a wave is given by the formula v = fλ, where f is the frequency and λ is the wavelength. Here, v = 500 Hz * 2 m = 1000 m/s.
Correct Answer: A — 1000 m/s
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Q. A wave travels through a medium with a speed of 300 m/s and has a frequency of 150 Hz. What is its wavelength?
A.
1 m
B.
2 m
C.
3 m
D.
4 m
Show solution
Solution
Wavelength (λ) can be calculated using the formula λ = v/f. Here, λ = 300 m/s / 150 Hz = 2 m.
Correct Answer: B — 2 m
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Q. A wave travels through a medium with a speed of 300 m/s and has a frequency of 150 Hz. What is the wavelength?
A.
1 m
B.
2 m
C.
3 m
D.
4 m
Show solution
Solution
Wavelength λ = v/f = 300/150 = 2 m.
Correct Answer: B — 2 m
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Q. A wave travels through a medium with a speed of 300 m/s and has a frequency of 150 Hz. What is the wavelength of the wave?
A.
1 m
B.
2 m
C.
3 m
D.
4 m
Show solution
Solution
The wavelength λ can be calculated using the formula v = fλ. Thus, λ = v/f = 300 m/s / 150 Hz = 2 m.
Correct Answer: B — 2 m
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Q. A wave travels with a frequency of 500 Hz and a wavelength of 2 m. What is its speed?
A.
250 m/s
B.
1000 m/s
C.
500 m/s
D.
200 m/s
Show solution
Solution
The speed of the wave is given by v = fλ. Here, v = 500 Hz * 2 m = 1000 m/s.
Correct Answer: A — 250 m/s
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Q. A wave travels with a speed of 300 m/s and has a frequency of 150 Hz. What is its wavelength?
A.
1 m
B.
2 m
C.
3 m
D.
4 m
Show solution
Solution
Wavelength (λ) can be calculated using the formula λ = v/f. Here, λ = 300 m/s / 150 Hz = 2 m.
Correct Answer: B — 2 m
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Q. A weight is measured as 10 kg with a relative error of 0.1. What is the absolute error?
A.
1 kg
B.
0.1 kg
C.
0.5 kg
D.
0.2 kg
Show solution
Solution
Absolute error = Relative error * True value = 0.1 * 10 = 1 kg.
Correct Answer: A — 1 kg
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Q. A weight is measured to be 50 kg with a possible error of 1 kg. What is the percentage error in the measurement?
A.
2%
B.
1%
C.
0.5%
D.
5%
Show solution
Solution
Percentage error = (Absolute error / Measured value) * 100 = (1 / 50) * 100 = 2%
Correct Answer: A — 2%
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Q. A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at a rate of 2 rad/s², what will be its angular velocity after 5 seconds?
A.
20 rad/s
B.
10 rad/s
C.
30 rad/s
D.
0 rad/s
Show solution
Solution
Final angular velocity = initial angular velocity + (angular acceleration × time) = 10 + (2 × 5) = 20 rad/s.
Correct Answer: A — 20 rad/s
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Q. A wheel of radius R is rolling without slipping on a horizontal surface. What is the relationship between the linear velocity v of the center of the wheel and its angular velocity ω?
A.
v = Rω
B.
v = ω/R
C.
v = 2Rω
D.
v = ω/2R
Show solution
Solution
For rolling without slipping, the linear velocity v is related to angular velocity ω by the equation v = Rω.
Correct Answer: A — v = Rω
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Q. A wheel of radius R rolls on a flat surface. If it rolls without slipping, what is the distance traveled by the center of mass after one complete rotation?
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Solution
The distance traveled by the center of mass after one complete rotation is equal to the circumference of the wheel, which is 2πR.
Correct Answer: A — 2πR
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Q. A wheel of radius R rolls without slipping on a horizontal surface. If it rotates with an angular velocity ω, what is the linear velocity of the center of the wheel?
A.
Rω
B.
2Rω
C.
ω/R
D.
R/ω
Show solution
Solution
The linear velocity v of the center of the wheel is related to the angular velocity ω by the equation v = Rω.
Correct Answer: A — Rω
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Q. A wheel of radius R rolls without slipping on a horizontal surface. If the wheel has an angular velocity ω, what is the linear velocity of the center of the wheel?
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Solution
The linear velocity v of the center of the wheel is related to the angular velocity by v = Rω.
Correct Answer: A — Rω
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Q. A wire has a resistance of 10 ohms at 20°C. If the temperature coefficient of resistivity is 0.004/°C, what will be its resistance at 100°C?
A.
10.4 ohms
B.
12 ohms
C.
14 ohms
D.
16 ohms
Show solution
Solution
R = R0(1 + α(T - T0)) = 10(1 + 0.004(100 - 20)) = 10(1 + 0.32) = 10.4 ohms.
Correct Answer: B — 12 ohms
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Q. A wire has a resistance of 10 Ω at 20°C. If the temperature coefficient of resistivity is 0.004/°C, what will be its resistance at 100°C?
A.
10 Ω
B.
12 Ω
C.
14 Ω
D.
16 Ω
Show solution
Solution
R = R0(1 + α(T - T0)) = 10(1 + 0.004(100 - 20)) = 10(1 + 0.32) = 10(1.32) = 13.2 Ω.
Correct Answer: C — 14 Ω
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Q. A wire has a resistance of 10 Ω at 20°C. If the temperature coefficient of resistivity is 0.004/°C, what will be the resistance at 100°C?
A.
10 Ω
B.
12 Ω
C.
14 Ω
D.
16 Ω
Show solution
Solution
R = R0(1 + α(T - T0)) = 10(1 + 0.004(100 - 20)) = 10(1 + 0.32) = 10(1.32) = 13.2 Ω.
Correct Answer: C — 14 Ω
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