ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Physical Optics and Thermodynamics (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. In a double-slit experiment λ = 600 nm, slit separation 0.30 mm and screen distance 1.5 m in air. If the whole apparatus is immersed in water (n = 4/3), the fringe width becomes
Answer: A. 2.25 mm
Explanation: In air β = λD/d = 3.0 mm. In water λ' = λ/n, so β' = 3.0/(4/3) = 2.25 mm.
Q2. In a double-slit experiment (λ = 600 nm) a thin transparent sheet of refractive index 1.5 and thickness 6 μm is placed over one slit. The central fringe shifts by
Answer: C. 5 fringe widths
Explanation: Extra optical path = (n − 1)t = 0.5 × 6 μm = 3 μm = 5λ, so the pattern shifts by 5 fringes.
Q3. In a double-slit experiment the fringe width is 2 mm. The distance from the central maximum to the third dark fringe is
Answer: D. 5 mm
Explanation: Dark fringes lie at (m + ½)β for m = 0, 1, 2…. The third dark fringe has m = 2: 2.5 × 2 = 5 mm.
Q4. Two coherent sources have intensity ratio 9 : 1. The ratio of the maximum to the minimum intensity in their interference pattern is
Answer: B. 4 : 1
Explanation: Amplitudes are in ratio 3 : 1. I_max/I_min = (3 + 1)²/(3 − 1)² = 16/4 = 4.
Q5. A non-reflecting coating of refractive index 1.25 is applied to glass of index 1.5 for light of wavelength 550 nm (in air). The minimum coating thickness is
Answer: A. 110 nm
Explanation: Both reflections occur at denser media, so destructive interference needs 2nt = λ/2, i.e. t = λ/4n = 550/(4 × 1.25) = 110 nm.
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Q6. A diffraction grating has 5000 lines per cm. For light of wavelength 590 nm the highest order of maximum that can be observed is
Q7. Light of wavelength 500 nm falls on a grating with 5000 lines per cm. The angle of the second-order maximum is
Q8. Light of wavelength 500 nm passes through a single slit 0.10 mm wide, and the pattern is seen on a screen 2.0 m away. The width of the central maximum is
Q9. Unpolarized light of intensity I₀ passes through three ideal polarizers whose axes are at 0°, 45° and 90° to the first. The emerging intensity is
Q10. Light is completely plane polarized on reflection from glass of refractive index √3. The angle of incidence is
Q11. X-rays of wavelength 0.10 nm are Bragg-reflected from crystal planes 0.28 nm apart. The highest order of reflection possible is
Q12. A movable mirror of a Michelson interferometer is displaced and 400 fringes cross the field of view. If λ = 600 nm, the displacement of the mirror is
Q13. In a Newton's rings experiment, the ratio of the diameter of the 25th dark ring to that of the 4th dark ring is
Q14. Light of wavelength 600 nm in air enters glass of refractive index 1.5. In the glass, its wavelength and frequency are
Q15. Two moles of a monatomic ideal gas are heated at constant pressure from 300 K to 400 K. Taking R = 8.3 J/mol K, the heat absorbed is
Q16. A gas undergoes a cycle represented on a P–V diagram by a right triangle: P rises at constant volume from 100 kPa to 300 kPa (at V = 3 L), then the gas returns along a straight line to (1 L, 100 kPa), and finally along a constant-pressure line to (3 L, 100 kPa). The net work per cycle has magnitude
Q17. A monatomic ideal gas at 300 K is compressed adiabatically to one-eighth of its original volume. The final temperature is
Q18. The rms speed of the molecules of an ideal gas at 27 °C is v. At what Celsius temperature will the rms speed be 2v?
Q19. Two moles of a diatomic ideal gas at 400 K have all translational and rotational modes active (vibration frozen). Taking R = 8.3 J/mol K, the internal energy is
Q20. A monatomic ideal gas expands at constant pressure. The fraction of the heat supplied that is converted into external work is
Q21. A 2 L vessel contains gas at 3 atm and is connected through a tap to a 4 L vessel containing the same gas at 6 atm, at the same temperature. After the tap is opened, the pressure is
Q22. A Carnot engine has its sink at 300 K and an efficiency of 25%. To double the efficiency, with the sink unchanged, the source temperature must be raised to
Q23. A Carnot refrigerator works between a freezer at 270 K and a room at 300 K. For 200 J of work input, the heat extracted from the freezer is
Q24. A heat engine absorbs 2000 J from the hot reservoir and rejects 1500 J to the cold reservoir in each cycle, completing 10 cycles per second. Its power output is
Q25. A quantity 600 J of heat flows by conduction from a large body at 400 K to a large body at 300 K. The net change in entropy of the two bodies is
Q26. Which of the following would violate the second law of thermodynamics?
Q27. 1 g of hydrogen gas (H₂, M = 2 g/mol) and 1 g of helium gas (He, M = 4 g/mol) are at the same temperature. The ratio of their total translational kinetic energies is
Q28. One mole of an ideal gas at 300 K expands isothermally to twice its volume (R = 8.3 J/mol K, ln2 = 0.69). The work done by the gas is about
Q29. The molar specific heat of an ideal gas during an isothermal process is
Q30. Two coherent sources of equal intensity I emit light of wavelength 500 nm. At a point P the path difference from the sources is 1.25 μm. The intensity at P is