ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Fluid Dynamics, Oscillations and Waves (Set 4): 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. Blood flows at 0.30 m/s in the aorta. The total cross-sectional area of all the capillaries is about 2000 times that of the aorta. The average blood speed in the capillaries is
Answer: D. 1.5 × 10⁻⁴ m/s
Explanation: Continuity: A₁v₁ = A₂v₂, so v₂ = 0.30/2000 = 1.5 × 10⁻⁴ m/s.
Q2. Water (density 1000 kg/m³) flows through a horizontal pipe, moving at 2 m/s in a wide section and 6 m/s in a narrow section. The pressure difference between the two sections is
Answer: C. 16 kPa
Explanation: Bernoulli: ΔP = ½ρ(v₂² − v₁²) = ½(1000)(36 − 4) = 16 000 Pa = 16 kPa.
Q3. A tank 1.0 m high stands on the ground and is full of water. A small hole is made in its side 0.8 m below the water surface. The horizontal distance from the tank at which the jet strikes the ground is (g = 10 m/s²)
Answer: A. 0.8 m
Explanation: Exit speed √(2gh) = 4 m/s. The hole is 0.2 m above the ground, so fall time = √(2 × 0.2/10) = 0.2 s. Range = 4 × 0.2 = 0.8 m.
Q4. Eight identical spherical raindrops, each with terminal velocity v, coalesce into a single drop. The terminal velocity of the large drop is
Answer: C. 4v
Explanation: Volume adds: R = 2r. Terminal velocity ∝ r² (since v = 2r²(ρ − σ)g/9η), so the large drop falls at 4v.
Q5. A small sphere of radius 1 mm moves at 0.02 m/s through oil of viscosity 0.5 Pa s. The viscous drag on it is
Answer: A. 6π × 10⁻⁵ N
Explanation: Stokes' law: F = 6πηrv = 6π(0.5)(10⁻³)(0.02) = 6π × 10⁻⁵ N.
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Q6. A particle in SHM has amplitude A. At what displacement from the mean position is its kinetic energy three times its potential energy?
Q7. A particle in SHM has a maximum speed of 2 m/s and a maximum acceleration of 8 m/s². Its amplitude is
Q8. A particle executes SHM with amplitude 5 cm and angular frequency 4 rad/s. When its displacement is 3 cm its speed is
Q9. A 1 kg mass is attached to two light springs, each of constant 200 N/m, joined end to end (in series) and the other end fixed. Its period of oscillation is
Q10. A spring of constant k is cut into two equal halves. A mass m suspended from one half oscillates with frequency f₂, while on the original spring it oscillates with f₁. The ratio f₂/f₁ is
Q11. A simple pendulum has period 1.5 s on the ground. Inside a lift that accelerates downward at 3g/4, its period becomes
Q12. The length of a seconds pendulum is increased by 1%. In a day this clock will lose about
Q13. A mass on a spring (k = 200 N/m) oscillates with amplitude 0.10 m. Its kinetic energy when the displacement is 0.06 m is
Q14. A travelling wave is described by y = 0.02 sin(100πt − 5πx) (SI units). Its speed is
Q15. At one point of a medium, a 10 Hz wave passes. The phase difference between the displacements at that point at two instants 0.05 s apart is
Q16. A stretched string under 100 N tension has fundamental frequency 50 Hz. The tension needed for its fundamental frequency to become 75 Hz (same length) is
Q17. A string 1.2 m long is fixed at both ends. Two consecutive resonant frequencies are found to be 150 Hz and 200 Hz. The speed of waves on the string is
Q18. A pipe closed at one end resonates at two successive frequencies 150 Hz and 250 Hz. Its fundamental frequency is
Q19. In a resonance tube experiment with a 500 Hz tuning fork, successive resonances occur at air-column lengths of 17 cm and 51 cm. The speed of sound is
Q20. A tuning fork of unknown frequency gives 4 beats per second with a 340 Hz fork. After a little wax is stuck on the unknown fork, the beat frequency falls to 2 per second. The original frequency was
Q21. A source emitting 480 Hz moves at 20 m/s toward an observer who moves at 10 m/s toward the source. Speed of sound = 340 m/s. The frequency heard is
Q22. The speed of sound in air at 27 °C is 340 m/s. Treating air as an ideal gas, its speed at 327 °C is about
Q23. Newton's isothermal formula gives the speed of sound in air as about 280 m/s. After applying Laplace's correction (γ = 1.4), the speed is about
Q24. Which of the following phenomena cannot be shown by sound waves travelling in air?
Q25. A pendulum bob swings with amplitude falling from 8 cm to 4 cm during the first 10 swings. Assuming exponential damping, the amplitude after 30 swings is
Q26. Air flows over the upper surface of an aeroplane wing at 80 m/s and under it at 60 m/s. Taking air density 1.2 kg/m³ and wing area 20 m², the lift force is
Q27. Water leaves a tap at 1 m/s and falls freely in a smooth stream. At a point 1.2 m below the tap the cross-sectional area of the stream is what fraction of that at the tap? (g = 10 m/s²)
Q28. A particle in SHM starts from the mean position at t = 0. The time it takes to first reach a displacement equal to half the amplitude is (T = period)
Q29. A small point source radiates sound uniformly in all directions. The amplitude of the wave at 6 m from the source compared with that at 2 m is
Q30. An open organ pipe is 0.85 m long and the speed of sound is 340 m/s. The frequency of its second overtone is