ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Fluid Dynamics, Oscillations and Waves (Set 7): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. Water flows at 1.5 m/s through a pipe of diameter 4 cm that narrows to a diameter of 2 cm. The speed in the narrow section is:
Answer: A. 6 m/s
Explanation: Continuity: A₁v₁ = A₂v₂, and area ∝ d², so v₂ = 1.5 × 4 = 6 m/s.
Q2. Water flows through a horizontal pipe, speed 2 m/s in a wide section and 6 m/s in a narrow section. Taking ρ = 1000 kg/m³, the pressure in the wide section exceeds that in the narrow section by:
Answer: C. 16 000 Pa
Explanation: Bernoulli: ΔP = ½ρ(v₂² − v₁²) = ½(1000)(36 − 4) = 16 000 Pa.
Q3. A tall open tank has a small hole 1.8 m below the water surface and 0.8 m above the horizontal ground. Taking g = 10 m/s², the water jet strikes the ground at a horizontal distance from the tank of:
Answer: B. 2.4 m
Explanation: v = √(2gh) = 6 m/s; fall time = √(2 × 0.8/10) = 0.4 s; x = 6 × 0.4 = 2.4 m.
Q4. A steel ball of radius 3 mm and density 8000 kg/m³ falls through a liquid of density 1000 kg/m³ and viscosity 1.4 Pa s. Taking g = 10 m/s², its terminal velocity is:
Answer: C. 0.1 m/s
Explanation: v_t = 2r²(ρ − σ)g/(9η) = 2(9×10⁻⁶)(7000)(10)/(12.6) = 0.1 m/s.
Q5. Water (ρ = 1000 kg/m³) flows steadily upward through a vertical pipe of uniform diameter. The gauge pressure at the lower point is 3.0 × 10⁵ Pa. Taking g = 10 m/s², the pressure at a point 10 m higher is:
Answer: A. 2.0 × 10⁵ Pa
Explanation: Equal speeds, so P₁ − P₂ = ρgh = 1000 × 10 × 10 = 1.0 × 10⁵ Pa; P₂ = 2.0 × 10⁵ Pa.
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Q6. A particle moves with SHM x = 0.2 sin(5t) in SI units. Its speed when its displacement is 0.12 m is:
Q7. A body executes SHM of amplitude A. At a displacement of A/2 from the mean position, the fraction of its total energy that is kinetic is:
Q8. A mass of 0.5 kg on a light spring of constant 200 N/m has period T. If the mass is changed to 2 kg, the new period (in terms of T) is:
Q9. A simple pendulum is inside a lift that accelerates downward at 7.5 m/s². Taking g = 10 m/s², the pendulum's period compared with its period in the stationary lift is:
Q10. A sound wave of speed 340 m/s and frequency 340 Hz travels along a line. Two points on the line, 0.25 m apart, have a phase difference of:
Q11. A travelling wave is described by y = 0.02 sin(4πx − 200πt) with x and y in metres and t in seconds. The speed of the wave is:
Q12. A string of length 0.8 m and mass per unit length 0.01 kg/m is fixed at both ends under a tension of 100 N. Its fundamental frequency is:
Q13. A string 1.2 m long fixed at both ends vibrates in its third harmonic. The wavelength of the stationary wave is:
Q14. A pipe closed at one end is 0.85 m long and the speed of sound is 340 m/s. The frequency of its first overtone is:
Q15. An unknown fork gives 5 beats per second with a 400 Hz fork. When the unknown fork is filed slightly (raising its frequency), the beat frequency falls to 3 per second. The original frequency of the unknown fork was:
Q16. A source of frequency 600 Hz moves at 85 m/s directly towards a stationary listener. Taking the speed of sound as 340 m/s, the listener hears:
Q17. The speed of sound in an ideal gas is proportional to the square root of the absolute temperature. The ratio of its speed at 327°C to that at 27°C is:
Q18. A sound wave travels from air into water. Which of its properties remains unchanged on crossing the boundary?
Q19. A child on a swing is pushed repeatedly at intervals equal to the swing's natural period. The amplitude grows large because of:
Q20. The amplitude of a damped oscillator falls exponentially and halves every 4 s. Its amplitude after 12 s, as a fraction of the initial value, is:
Q21. Air flowing over an aircraft wing of area 20 m² creates a pressure difference of 250 Pa between the lower and upper surfaces. The net lift force is:
Q22. In a Venturi meter the main pipe has 4 times the cross-sectional area of the throat. Water (ρ = 1000 kg/m³) moves at 0.5 m/s in the main pipe. The pressure drop between the main pipe and the throat is:
Q23. Water moves at 0.5 m/s along a pipe of cross-section 8 cm². The volume flow rate is:
Q24. A mass hung on a light vertical spring stretches it by 0.1 m at equilibrium. Taking g = 10 m/s², the period of its vertical oscillations is:
Q25. For SHM written as x = A sin(ωt + φ) with φ between 0 and 2π, the particle at t = 0 is at x = A/2 and is moving towards the positive x-direction. The phase constant φ is:
Q26. A particle in SHM has period 12 s. Starting from the mean position, the time taken to reach a displacement equal to half of the amplitude is:
Q27. Adjacent nodes of a stationary wave on a string are 0.3 m apart and the string vibrates at 200 Hz. The speed of the travelling waves forming it is:
Q28. In a stationary wave on a string fixed at both ends, particles between two successive nodes:
Q29. An open organ pipe has a fundamental frequency of 600 Hz. If one end is closed, keeping the same length and conditions, the fundamental frequency becomes:
Q30. Two identical-density spheres fall through the same viscous liquid, each reaching terminal velocity. If sphere B has twice the radius of sphere A, then v_B/v_A is (neglect the liquid's own density):