ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Fluid Dynamics, Oscillations and Waves (Set 5): 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 leaves a tap with a speed of 3 m s⁻¹ and falls as a smooth, narrowing stream. At a point 0.8 m below the tap outlet (g = 10 m s⁻²), the cross-sectional area of the stream compared with the area at the outlet is:
Answer: C. 0.6 times
Explanation: v² = 3² + 2(10)(0.8) = 25, so v = 5 m/s. Continuity: A₁v₁ = A₂v₂, so A₂/A₁ = 3/5 = 0.6.
Q2. Air flows over the top surface of an aircraft wing at 70 m s⁻¹ and under it at 60 m s⁻¹. Take air density 1.2 kg m⁻³ and wing area 20 m². The net upward lift from this pressure difference is:
Answer: A. 15.6 kN
Explanation: Δp = ½ρ(v₁² − v₂²) = 0.6(4900 − 3600) = 780 Pa. Lift = 780 × 20 = 15 600 N = 15.6 kN.
Q3. A tall open tank 2 m deep is full of water. A small hole 0.5 m below the water surface gives a horizontal jet that lands at a certain distance from the tank. A second hole at which depth below the surface would give the same horizontal range?
Answer: C. 1.5 m
Explanation: Range = 2√(h(H − h)) is symmetric in h and H − h. For h = 0.5 m, H − h = 1.5 m gives the same range.
Q4. A sealed tank holds water with air above it at a gauge pressure of 40 kPa (above the atmosphere outside). A small hole is made in its side 1 m below the water surface (g = 10 m s⁻², ρ = 1000 kg m⁻³). The speed of efflux is:
Answer: B. 10 m s⁻¹
Explanation: v = √(2(P_g/ρ + gh)) = √(2(40 + 10)) = √100 = 10 m/s.
Q5. A sphere of radius 2 mm and density 1900 kg m⁻³ falls through a liquid of density 1000 kg m⁻³ and viscosity 0.4 Pa s (g = 10 m s⁻²). Using Stokes' law, its terminal velocity is:
Answer: C. 2 cm s⁻¹
Explanation: v_t = 2r²(ρ_s − ρ)g/(9η) = 2(4×10⁻⁶)(900)(10)/(9×0.4) = 0.072/3.6 = 0.02 m/s = 2 cm/s.
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Q6. A particle executes SHM with displacement x = 0.1 sin(20πt) in metres. The maximum acceleration is:
Q7. A body in SHM has amplitude 0.4 m and angular frequency 5 rad s⁻¹. Its speed when it is 0.2 m from the mean position is:
Q8. A particle in SHM with period 24 s starts from the mean position. The time it takes to reach a displacement equal to half the amplitude is:
Q9. A 3 kg mass is attached to two springs of constants 100 N m⁻¹ and 300 N m⁻¹ joined end to end (in series) and set oscillating. The angular frequency of its oscillation is:
Q10. A mass hanging from a spring oscillates with period 2 s. The spring is cut into four equal parts and the same mass is hung from one part. The new period is:
Q11. A mass hung from a vertical spring stretches it 0.4 m at equilibrium (g = 10 m s⁻²). If pulled down slightly and released, the period of oscillation is:
Q12. A pendulum clock keeps correct time. Because of warm weather the pendulum's length increases by 2 %. Approximately how much time will the clock lose in one day (86 400 s)?
Q13. A simple pendulum is in a lift that accelerates downward at 7.5 m s⁻² (g = 10 m s⁻²). The ratio of its period in the lift to its period at rest, T′/T, is:
Q14. A 0.5 kg bob on a 1.6 m string is released from rest with the string making 60° with the vertical (g = 10 m s⁻²). The tension in the string as the bob passes its lowest point is:
Q15. In SHM of amplitude A, the kinetic energy is three times the potential energy when the displacement is:
Q16. A 0.2 kg body executes SHM with amplitude 5 cm and angular frequency 10 rad s⁻¹. Its total energy is:
Q17. A system is driven at its natural frequency. If the damping is then increased, the amplitude at resonance:
Q18. A progressive wave on a string is described by y = 0.01 sin(20πt − 4πx), with x and y in metres and t in seconds. The speed of the wave is:
Q19. A taut string of length 2 m and mass 5 g is fixed at both ends and held at a tension of 25 N. Its fundamental frequency is:
Q20. A string fixed at both ends has a fundamental frequency of 50 Hz. Its tension is increased by 21 % with no change in length. The new fundamental frequency is:
Q21. An open organ pipe has a fundamental frequency of 400 Hz. One end is now closed. The frequency of the second overtone of the closed pipe is:
Q22. Tuning fork A (256 Hz) is sounded with fork B and 4 beats per second are heard. When a little wax is put on a prong of B, the beat frequency falls to 2 per second. The original frequency of B was:
Q23. The speed of sound in air is 340 m s⁻¹. A source emits a note of 400 Hz while moving toward a listener at 20 m s⁻¹, and the listener moves toward the source at 20 m s⁻¹. The frequency heard is:
Q24. The speed of sound in air at 27 °C is 340 m s⁻¹. Treating air as an ideal gas, its speed at 327 °C is closest to:
Q25. Use v = (331 + 0.6 t) m s⁻¹ with t in °C. A person at 35 °C claps and hears the echo from a cliff 2.0 s later. The cliff is at a distance of:
Q26. A wave of speed 300 m s⁻¹ and frequency 200 Hz travels along a line. The phase difference between two points on the line 0.5 m apart is:
Q27. A stationary wave on a string has wavelength 0.4 m. The distance between the first and the fourth node along the string is:
Q28. A wave's amplitude is doubled and its frequency is also doubled, with everything else unchanged. The rate at which it transmits energy changes by a factor of:
Q29. Two coherent waves of amplitudes 3 units and 4 units meet at a point with a phase difference of π/2. The amplitude of the resultant is:
Q30. In a resonance-tube experiment with a 500 Hz fork, the first resonance occurs at an air-column length of 16 cm and the second at 50 cm. The speed of sound deduced is: