Engineering Entrance
Q. A solid cylinder rolls down an incline. If its height is h, what is its linear speed at the bottom? (2023)
A.
√(gh)
B.
√(2gh)
C.
√(3gh)
D.
√(4gh)
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Solution
Using conservation of energy, potential energy converts to kinetic energy. For a solid cylinder, v = √(2gh).
Correct Answer: B — √(2gh)
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Q. A solid sphere of radius R rolls without slipping down an incline of height h. What is its speed at the bottom of the incline? (2021)
A.
√(2gh)
B.
√(3gh)
C.
√(4gh)
D.
√(5gh)
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Solution
Using conservation of energy, potential energy at the top = kinetic energy at the bottom. For a solid sphere, v = √(5gh/7). Thus, speed at the bottom is √(3gh).
Correct Answer: B — √(3gh)
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Q. A solid sphere of radius R rolls without slipping down an inclined plane of height h. What is the speed of the center of mass at the bottom of the incline? (2021)
A.
√(2gh)
B.
√(3gh)
C.
√(4gh)
D.
√(5gh)
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Solution
Using conservation of energy, potential energy at height h = kinetic energy at the bottom. For a solid sphere, v = √(3gh).
Correct Answer: B — √(3gh)
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Q. A sound wave travels at a speed of 340 m/s and has a frequency of 1700 Hz. What is its wavelength? (2021)
A.
0.2 m
B.
0.5 m
C.
2 m
D.
1 m
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Solution
Wavelength (λ) = Speed (v) / Frequency (f) = 340 m/s / 1700 Hz = 0.2 m.
Correct Answer: A — 0.2 m
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Q. A sound wave travels through air at 343 m/s. If its frequency is 686 Hz, what is its wavelength? (2023)
A.
0.5 m
B.
1 m
C.
2 m
D.
3 m
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Solution
Wavelength λ = v/f = 343 m/s / 686 Hz = 0.5 m.
Correct Answer: A — 0.5 m
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Q. A sound wave travels through air at a speed of 340 m/s. If the frequency of the sound is 170 Hz, what is the wavelength?
A.
1 m
B.
2 m
C.
3 m
D.
4 m
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Solution
The wavelength λ is given by λ = v/f. Thus, λ = 340/170 = 2 m.
Correct Answer: B — 2 m
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Q. A stone is thrown horizontally from a height of 45 m. How long will it take to hit the ground? (Take g = 10 m/s²) (2023)
A.
3 s
B.
4.5 s
C.
5 s
D.
6 s
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Solution
Using h = 0.5 * g * t^2, we have 45 = 0.5 * 10 * t^2. Solving gives t^2 = 9, so t = 3 s.
Correct Answer: A — 3 s
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Q. A train moving at 72 km/h applies brakes and comes to a stop in 5 seconds. What is the deceleration? (2023)
A.
2 m/s²
B.
3 m/s²
C.
4 m/s²
D.
5 m/s²
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Solution
First convert speed to m/s: 72 km/h = 20 m/s. Deceleration = (final velocity - initial velocity) / time = (0 - 20) / 5 = -4 m/s².
Correct Answer: C — 4 m/s²
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Q. A tuning fork produces a sound wave of frequency 440 Hz. What is the period of the wave? (2019)
A.
0.00227 s
B.
0.005 s
C.
0.01 s
D.
0.001 s
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Solution
Period T = 1/f = 1/440 Hz ≈ 0.00227 s.
Correct Answer: A — 0.00227 s
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Q. A tuning fork produces a sound wave of frequency 440 Hz. What is the time period of this sound wave? (2021)
A.
0.00227 s
B.
0.0045 s
C.
0.01 s
D.
0.005 s
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Solution
Time period (T) = 1/f = 1/440 Hz ≈ 0.00227 s.
Correct Answer: A — 0.00227 s
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Q. A tuning fork produces a sound wave of frequency 440 Hz. What is the time period of the sound wave?
A.
0.00227 s
B.
0.005 s
C.
0.01 s
D.
0.02 s
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Solution
The time period T is the reciprocal of frequency f. Thus, T = 1/f = 1/440 ≈ 0.00227 s.
Correct Answer: A — 0.00227 s
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Q. A tuning fork vibrates at a frequency of 440 Hz. What is the time period of the fork? (2020)
A.
0.00227 s
B.
0.0045 s
C.
0.01 s
D.
0.005 s
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Solution
Time period T = 1/f = 1/440 Hz ≈ 0.00227 s.
Correct Answer: A — 0.00227 s
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Q. A uniform rod of length L is pivoted at one end and released from rest. What is the angular speed when it reaches the vertical position? (2019)
A.
√(3g/L)
B.
√(2g/L)
C.
√(g/L)
D.
√(4g/L)
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Solution
Using conservation of energy, potential energy converts to rotational kinetic energy. Angular speed ω = √(3g/L).
Correct Answer: B — √(2g/L)
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Q. A uniform rod of length L is pivoted at one end and released from rest. What is the angular speed just before it hits the ground? (2019)
A.
√(3g/L)
B.
√(2g/L)
C.
√(g/L)
D.
√(4g/L)
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Solution
Using conservation of energy, potential energy converts to rotational kinetic energy. Angular speed ω = √(3g/L).
Correct Answer: B — √(2g/L)
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Q. A vehicle travels with a uniform speed of 60 km/h. How far will it travel in 2 hours? (2023)
A.
80 km
B.
100 km
C.
120 km
D.
140 km
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Solution
Distance = speed * time = 60 km/h * 2 h = 120 km.
Correct Answer: C — 120 km
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Q. A wave has a frequency of 10 Hz and a wavelength of 5 m. What is its speed? (2020)
A.
50 m/s
B.
10 m/s
C.
2 m/s
D.
5 m/s
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Solution
Speed (v) = frequency (f) × wavelength (λ) = 10 Hz × 5 m = 50 m/s.
Correct Answer: A — 50 m/s
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Q. A wave has a frequency of 500 Hz and a wavelength of 0.6 m. What is the speed of the wave? (2022)
A.
300 m/s
B.
500 m/s
C.
600 m/s
D.
400 m/s
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Solution
Using the wave equation v = fλ, we find v = 500 Hz * 0.6 m = 300 m/s.
Correct Answer: A — 300 m/s
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Q. A wave has a frequency of 60 Hz and a wavelength of 3 m. What is its speed? (2016)
A.
180 m/s
B.
120 m/s
C.
60 m/s
D.
90 m/s
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Solution
Speed v = f × λ = 60 Hz × 3 m = 180 m/s.
Correct Answer: A — 180 m/s
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Q. A wave has a frequency of 60 Hz and a wavelength of 3 m. What is the speed of the wave?
A.
180 m/s
B.
120 m/s
C.
60 m/s
D.
30 m/s
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Solution
The speed v of a wave is given by v = fλ. Thus, v = 60 * 3 = 180 m/s.
Correct Answer: B — 120 m/s
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Q. A wave has a speed of 300 m/s and a frequency of 150 Hz. What is its wavelength? (2022)
A.
1 m
B.
2 m
C.
3 m
D.
4 m
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Solution
Wavelength λ can be calculated using the formula λ = v/f. Therefore, λ = 300 m/s / 150 Hz = 2 m.
Correct Answer: B — 2 m
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Q. A wave on a string has a speed of 50 m/s and a wavelength of 2 m. What is its frequency? (2018)
A.
25 Hz
B.
50 Hz
C.
100 Hz
D.
75 Hz
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Solution
Frequency f = v/λ = 50 m/s / 2 m = 25 Hz.
Correct Answer: A — 25 Hz
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Q. A wave on a string is described by the equation y(x, t) = 0.05 sin(2π(0.1x - 5t)). What is the amplitude of the wave?
A.
0.01 m
B.
0.05 m
C.
0.1 m
D.
0.2 m
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Solution
The amplitude of the wave is the coefficient in front of the sine function. Here, the amplitude is 0.05 m.
Correct Answer: B — 0.05 m
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Q. A wave traveling along a string has a frequency of 50 Hz and a wavelength of 2 m. What is the speed of the wave? (2020)
A.
25 m/s
B.
50 m/s
C.
100 m/s
D.
75 m/s
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Solution
Speed (v) = frequency (f) × wavelength (λ) = 50 Hz × 2 m = 100 m/s.
Correct Answer: C — 100 m/s
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Q. A wave travels in a medium with a speed of 300 m/s and has a frequency of 75 Hz. What is the wavelength? (2021)
A.
4 m
B.
2 m
C.
3 m
D.
1 m
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Solution
Wavelength λ = v/f = 300 m/s / 75 Hz = 4 m.
Correct Answer: A — 4 m
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Q. A wave travels through a medium with a speed of 500 m/s and has a wavelength of 2 m. What is its frequency? (2022)
A.
250 Hz
B.
500 Hz
C.
1000 Hz
D.
2000 Hz
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Solution
Using the wave equation v = fλ, we can find frequency f = v/λ = 500 m/s / 2 m = 250 Hz.
Correct Answer: A — 250 Hz
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Q. A wave travels with a speed of 340 m/s and has a frequency of 170 Hz. What is its wavelength? (2022)
A.
2.0 m
B.
1.0 m
C.
0.5 m
D.
3.0 m
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Solution
Wavelength λ = v/f = 340 m/s / 170 Hz = 2.0 m.
Correct Answer: A — 2.0 m
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Q. A wheel of radius 0.5 m is rotating with an angular speed of 10 rad/s. What is the linear speed of a point on the edge of the wheel? (2022)
A.
5 m/s
B.
10 m/s
C.
15 m/s
D.
20 m/s
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Solution
Linear speed v = rω = 0.5 m * 10 rad/s = 5 m/s.
Correct Answer: B — 10 m/s
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Q. A wheel rotates with a constant angular acceleration α. If its initial angular velocity is ω₀, what is its angular velocity after time t? (2023)
A.
ω₀ + αt
B.
ω₀ - αt
C.
αt²
D.
ω₀t
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Solution
Using the equation of motion for rotation, ω = ω₀ + αt.
Correct Answer: A — ω₀ + αt
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Q. An object is dropped from a height of 80 m. How long will it take to reach the ground? (Take g = 10 m/s²) (2023)
A.
4 s
B.
8 s
C.
10 s
D.
12 s
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Solution
Using the formula: h = 0.5 * g * t^2. Rearranging gives t = sqrt(2h/g) = sqrt(2*80/10) = sqrt(16) = 4 s.
Correct Answer: B — 8 s
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Q. An object moves with a constant velocity of 10 m/s. What is the net force acting on it? (2023)
A.
0 N
B.
10 N
C.
20 N
D.
100 N
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Solution
If the object moves with constant velocity, the net force acting on it is 0 N.
Correct Answer: A — 0 N
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