ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Fluid Dynamics, Oscillations and Waves (Set 6): 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 3 m/s through a main pipe of cross-section 0.04 m². It then splits equally into three identical branch pipes, each of cross-section 0.01 m². The speed of water in each branch is
Answer: B. 4 m/s
Explanation: Continuity: 0.04×3 = 3×0.01×v, so v = 4 m/s.
Q2. In a U-tube, a 20 cm column of water balances a column of oil of density 0.80 g/cm³ (water 1.00 g/cm³), both measured above the common interface. The height of the oil column is
Answer: C. 25 cm
Explanation: Equal pressures: 1.00×20 = 0.80×h, so h = 25 cm.
Q3. Water (density 1000 kg/m³) flows steadily through a horizontal pipe. Where the speed is 2 m/s the pressure is higher than where the speed is 6 m/s. The pressure difference is
Answer: B. 16 kPa
Explanation: Bernoulli: ΔP = ½ρ(v₂² − v₁²) = 500×32 = 16000 Pa = 16 kPa.
Q4. A tall tank of water, 1.0 m deep and standing on the ground, has a small hole 0.2 m below the water surface. At what depth below the surface should a second small hole be made to give the same horizontal range on the ground? (Keep the tank full.)
Answer: C. 0.8 m
Explanation: Range = 2√(h(H − h)) is symmetric in h and H − h (range 0.8 m), so the second hole is at depth 1.0 − 0.2 = 0.8 m.
Q5. An oil drop of radius 1.0×10⁻⁵ m and density 900 kg/m³ falls steadily through air of viscosity 1.8×10⁻⁵ Pa s. Neglect air density and use v = 2r²ρg/(9η). The terminal speed in mm/s is
Answer: A. 11.1 mm/s
Explanation: v = 2(10⁻¹⁰)(900)(10)/(9×1.8×10⁻⁵) = 0.01111 m/s = 11.1 mm/s.
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Q6. A particle executes SHM with amplitude 0.04 m and angular frequency 10 rad/s. Its speed when its displacement is 0.02 m is
Q7. A particle in SHM has a period of 2.4 s. Starting at the equilibrium position, the time it takes to reach half its amplitude is
Q8. A 0.25 kg mass is attached between two springs, k₁ = 100 N/m and k₂ = 300 N/m, so that both springs are stretched or compressed together when it moves (equivalent to parallel springs). The period of oscillation is
Q9. A simple pendulum has period 2.0 s at rest on the ground (g = 10 m/s²). It is hung inside a closed truck which accelerates horizontally at 7.5 m/s². The period of small oscillations about its new equilibrium position is
Q10. The length of a simple pendulum is increased by 21%. The period increases by
Q11. A body in SHM has amplitude 8 cm. At what displacement from the mean position is its potential energy one-quarter of its total energy?
Q12. A damped oscillator's amplitude halves every 3 oscillations. After 6 oscillations the fraction of its initial energy that remains is
Q13. A lightly damped oscillator is driven by a periodic force. Increasing the damping (all else unchanged) has what effect on the amplitude–frequency curve near resonance?
Q14. A stretched string fixed at both ends has fundamental frequency f. If its tension is made four times larger and its length is halved, the new fundamental frequency is
Q15. A string fixed at both ends resonates at 90 Hz with three antinodes. The next higher frequency at which it can resonate is
Q16. A pipe closed at one end has a fundamental frequency of 85 Hz (speed of sound 340 m/s). Counting the fundamental as the first resonance, its third resonant frequency is
Q17. In a resonance-tube experiment with a tuning fork of 400 Hz, successive resonances occur at air-column lengths of 21.25 cm and 63.75 cm. The speed of sound is
Q18. Fork A has frequency 256 Hz and gives 4 beats per second with fork B. When B is loaded with a little wax, the beats become 6 per second. The original frequency of B is
Q19. A source of frequency 640 Hz and an observer move directly toward each other at 20 m/s and 10 m/s respectively relative to the still air (speed of sound 340 m/s). The observed frequency is
Q20. A wave is described by y = 0.5 sin[2π(t/0.02 − x/4)] with x in metres and t in seconds. Its speed is
Q21. A wave of frequency 200 Hz travels at 240 m/s. The phase difference between two points on the wave 0.15 m apart along the direction of travel is
Q22. In a hydraulic press the small piston has area 10 cm² and the large piston has area 500 cm². A force of 40 N on the small piston can support a load on the large piston of
Q23. A wooden cube of side 10 cm and density 600 kg/m³ floats in water (1000 kg/m³). What is the largest mass that can be placed on top of the cube without submerging it any deeper than just flush with the water surface?
Q24. Air (density 1.2 kg/m³) flows over the top of an aircraft wing at 80 m/s and under it at 60 m/s. The wing area is 20 m². Using Bernoulli's equation, the net upward force from the pressure difference is
Q25. The speed of sound in an ideal gas is proportional to the square root of its absolute temperature. By what factor does it increase when the gas is heated from 27 °C to 327 °C?
Q26. Which of the following waves cannot be polarized?
Q27. A stationary wave of frequency 85 Hz is set up in air (speed 340 m/s). The distance between the 1st and the 4th node is
Q28. A mass hung on a vertical spring stretches it by 2.5 cm at equilibrium. When pulled down slightly and released, it oscillates with angular frequency (g = 10 m/s²)
Q29. A 0.10 kg particle executes SHM of amplitude 0.20 m with angular frequency 10 rad/s. Its total energy is
Q30. A light spring supporting a mass oscillates at frequency f. The spring is cut into two equal halves and the same mass is attached to one half. The new frequency is