ECAT — Engineering College Admission Test (UET)

ECAT Physics — Fluid Dynamics, Oscillations and Waves (Set 1)

Take the ECAT Physics — Fluid Dynamics, Oscillations and Waves (Set 1): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer…

What this test covers

• 30 ECAT Physics

Sample questions with answers

The first 5 questions of this test, with the correct answer and explanation.

1. Q1. Water flows at 2 m/s through a pipe of cross-section 4 cm². The pipe narrows to 1 cm². What is the speed in the narrow part?

   • A. 4 m/s
   • B. 8 m/s ✓
   • C. 16 m/s
   • D. 0.5 m/s

   Answer: B. 8 m/s

   Explanation: Equation of continuity: A₁v₁ = A₂v₂, so v₂ = 4 × 2/1 = 8 m/s.

2. Q2. If the diameter of a pipe carrying an incompressible fluid is halved at a constriction, the flow speed there becomes:

   • A. one quarter
   • B. half
   • C. twice
   • D. four times ✓

   Answer: D. four times

   Explanation: A ∝ d², so halving d makes A one quarter; by Av = constant, v becomes four times.

3. Q3. A large open water tank has a small hole 5 m below the water surface. With what speed does water emerge from the hole? (g = 10 m/s²)

   • A. 50 m/s
   • B. 100 m/s
   • C. 5 m/s
   • D. 10 m/s ✓

   Answer: D. 10 m/s

   Explanation: Torricelli's theorem: v = √(2gh) = √100 = 10 m/s.

4. Q4. A small sphere falls through a viscous liquid. If its radius is doubled (same material), its terminal velocity becomes:

   • A. twice
   • B. eight times
   • C. four times ✓
   • D. half

   Answer: C. four times

   Explanation: At terminal velocity, weight − upthrust = 6πηrv; the left side ∝ r³, so v ∝ r².

5. Q5. According to Bernoulli's equation for a horizontal streamline, where the speed of a fluid is greater:

   • A. its pressure is higher
   • B. its pressure does not change
   • C. its pressure is lower ✓
   • D. its density increases

   Answer: C. its pressure is lower

   Explanation: P + ½ρv² = constant along a horizontal streamline, so higher v means lower P (as in a venturi meter or aircraft wing).

The other 25 questions

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6. Q6. Which statement about streamline (laminar) flow is correct?

   • A. Streamlines never cross each other
   • B. It occurs only at very high speeds
   • C. Fluid layers mix randomly
   • D. The velocity at a point keeps changing with time

7. Q7. Water flows at 0.2 m/s through a pipe of cross-sectional area 0.05 m². What is the volume flow rate?

   • A. 1 litre per second
   • B. 10 litres per second
   • C. 0.25 litres per second
   • D. 4 litres per second

8. Q8. Water (density 1000 kg/m³) flows through a horizontal pipe. Its speed increases from 2 m/s to 4 m/s at a constriction. What is the pressure difference between the wide and narrow parts?

   • A. 6000 Pa
   • B. 2000 Pa
   • C. 1000 Pa
   • D. 8000 Pa

9. Q9. A 2 kg mass is attached to a spring of spring constant 200 N/m and set into simple harmonic motion. What is its period?

   • A. 2π s
   • B. π/10 s
   • C. π/5 s
   • D. 10π s

10. Q10. If the length of a simple pendulum is made four times greater, its period becomes:

    • A. four times
    • B. unchanged
    • C. twice
    • D. half

11. Q11. A pendulum has a period of 2 s on Earth. What is its period on a planet where the acceleration due to gravity is one quarter of Earth's?

    • A. 1 s
    • B. 0.5 s
    • C. 4 s
    • D. 8 s

12. Q12. A particle performs SHM with amplitude 0.1 m and angular frequency 20 rad/s. What is its maximum speed?

    • A. 40 m/s
    • B. 200 m/s
    • C. 2 m/s
    • D. 0.2 m/s

13. Q13. A body executes SHM with amplitude 5 cm and angular frequency 20 rad/s. What is its maximum acceleration?

    • A. 1 m/s²
    • B. 20 m/s²
    • C. 10 m/s²
    • D. 2000 m/s²

14. Q14. For a body in SHM, what fraction of the total energy is kinetic when the displacement is half the amplitude?

    • A. 3/4
    • B. 1/4
    • C. 1/2
    • D. 1/3

15. Q15. A mass hung from a spring stretches it by 10 cm at equilibrium. If the mass is pulled down slightly and released, what is the period of oscillation? (g = 10 m/s²)

    • A. 0.02π s
    • B. 0.2π s
    • C. 0.1π s
    • D. 2π s

16. Q16. In SHM, the phase difference between the displacement and the velocity of the particle is:

    • A. 2π
    • B. π
    • C. zero
    • D. π/2

17. Q17. Resonance occurs in a driven oscillating system when:

    • A. the driving force is very large
    • B. the damping is very large
    • C. the driving frequency equals the natural frequency of the system
    • D. the driving frequency is twice the natural frequency

18. Q18. Increasing the damping in a driven oscillator makes the resonance curve:

    • A. unchanged in shape
    • B. flatter, with a smaller peak amplitude
    • C. shift to a much higher frequency
    • D. sharper, with a larger peak amplitude

19. Q19. A sound wave of frequency 680 Hz travels through air at 340 m/s. What is its wavelength?

    • A. 0.25 m
    • B. 0.5 m
    • C. 2 m
    • D. 1 m

20. Q20. A string under a tension of 100 N has a mass per unit length of 0.01 kg/m. What is the speed of transverse waves on it?

    • A. 100 m/s
    • B. 10 m/s
    • C. 1000 m/s
    • D. 10000 m/s

21. Q21. In a stationary wave of wavelength λ, how far is a node from the nearest antinode?

    • A. λ/4
    • B. λ/2
    • C. 2λ
    • D. λ

22. Q22. A string 1 m long is fixed at both ends. Transverse waves travel on it at 200 m/s. What is its fundamental frequency?

    • A. 400 Hz
    • B. 100 Hz
    • C. 200 Hz
    • D. 50 Hz

23. Q23. An organ pipe closed at one end is 0.85 m long. If the speed of sound is 340 m/s, what is its fundamental frequency?

    • A. 400 Hz
    • B. 200 Hz
    • C. 100 Hz
    • D. 50 Hz

24. Q24. Which statement about a pipe closed at one end is correct?

    • A. It produces only even harmonics
    • B. Its fundamental frequency is higher than that of an open pipe of the same length
    • C. It produces all harmonics
    • D. It produces only odd harmonics of its fundamental

25. Q25. An unknown tuning fork gives 4 beats per second with a 256 Hz fork. When the unknown fork is loaded with a little wax, the beat rate falls to 2 per second. What was the original frequency of the unknown fork?

    • A. 260 Hz
    • B. 258 Hz
    • C. 254 Hz
    • D. 252 Hz

26. Q26. A source emitting 600 Hz moves directly towards a stationary listener at 40 m/s. If the speed of sound is 340 m/s, what frequency does the listener hear?

    • A. 540 Hz
    • B. 530 Hz
    • C. 670 Hz
    • D. 680 Hz

27. Q27. The speed of sound in a gas is 340 m/s. If the absolute temperature of the gas is made four times greater, the speed of sound becomes:

    • A. 680 m/s
    • B. 1360 m/s
    • C. 170 m/s
    • D. 340 m/s

28. Q28. Laplace corrected Newton's formula for the speed of sound in air by assuming that sound propagation is:

    • A. isochoric, so v = √(γρ/P)
    • B. isobaric, so v = √(ρ/P)
    • C. isothermal, so v = √(P/ρ)
    • D. adiabatic, so v = √(γP/ρ)

29. Q29. Which property shows that sound waves in air are longitudinal and not transverse?

    • A. Sound waves cannot be polarized
    • B. Sound waves can be reflected
    • C. Sound waves can interfere
    • D. Sound waves can be diffracted

30. Q30. Two points on a progressive wave of wavelength 1 m are 0.25 m apart along the direction of travel. What is the phase difference between them?

    • A. π/4 rad
    • B. π/2 rad
    • C. 2π rad
    • D. π rad