ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Physical Optics and Thermodynamics (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. In a double-slit experiment with slit separation 0.5 mm and a screen 1.5 m away, the 10th bright fringe lies 15 mm from the central maximum. The wavelength of the light is:
Answer: A. 500 nm
Explanation: Fringe width β = 15/10 = 1.5 mm. λ = βd/D = (1.5×10⁻³)(0.5×10⁻³)/1.5 = 5 × 10⁻⁷ m = 500 nm.
Q2. In a double-slit experiment, a thin transparent sheet of refractive index 1.5 and thickness 6 μm is placed over one slit. For light of wavelength 600 nm, the central fringe moves through how many fringe widths?
Answer: C. 5
Explanation: Extra optical path = (n − 1)t = 0.5 × 6 μm = 3 μm. Shift in fringes = 3000 nm/600 nm = 5.
Q3. Light of wavelength 500 nm falls on a single slit of width 0.1 mm. On a screen 2 m from the slit, the width of the central bright maximum is:
Answer: B. 2 cm
Explanation: First minima occur at sinθ = λ/a = 5 × 10⁻³. Central maximum width = 2λD/a = 2(5×10⁻⁷)(2)/10⁻⁴ = 0.02 m = 2 cm.
Q4. A diffraction grating has 5000 lines per cm. For light of wavelength 600 nm, the maximum order of the spectrum that can be observed is:
Answer: B. 3
Explanation: d = 1/5000 cm = 2 × 10⁻⁶ m. sinθ = mλ/d ≤ 1 gives m ≤ 2000/600 = 3.33, so the highest observable order is 3.
Q5. Unpolarised light of intensity I₀ passes through two polarisers whose axes are at 90° to each other. A third polariser, with its axis at 30° to the first, is inserted between them. The final intensity transmitted is:
Answer: B. 3I₀/32
Explanation: After the first: I₀/2. Second (30°): (I₀/2)cos²30° = 3I₀/8. Third (60° from second): (3I₀/8)cos²60° = 3I₀/32.
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Q6. Light incident on a transparent material of refractive index √3 at the polarising (Brewster) angle is reflected as completely plane-polarised light. The angle of refraction in the material is:
Q7. A glass lens (n = 1.5) is coated with a thin layer of a material of refractive index 1.38 to reduce reflection of light of wavelength 552 nm. The minimum thickness of the coating is:
Q8. In a Newton's rings arrangement, a lens of radius of curvature 0.9 m rests on a flat plate and is illuminated by light of wavelength 500 nm. The radius of the 20th dark ring is:
Q9. X-rays of wavelength 0.1 nm are reflected in second order at a glancing angle of 30° from a family of crystal planes. The spacing between the planes is:
Q10. In a Michelson interferometer, 300 bright fringes cross the field of view while the movable mirror is displaced by 0.075 mm. The wavelength of the light used is:
Q11. Two coherent point sources vibrating in phase emit light of wavelength 600 nm. At a point the path difference to the two sources is 1.5 μm. The interference there is:
Q12. Two coherent sources give equal-intensity waves; each alone would produce intensity I₀ at a point P. At a point where the phase difference between the waves is 120°, the resultant intensity is:
Q13. A grating is illuminated with white light. At a certain angle the second-order image of 600 nm light coincides with an image of 400 nm light. The order of the 400 nm image is:
Q14. Which condition is necessary to obtain a stable (sustained) interference pattern from two sources?
Q15. Two moles of a monatomic ideal gas are heated at constant pressure by 10 K (R = 8.31 J mol⁻¹ K⁻¹). The increase in its internal energy is:
Q16. A gas is taken through a clockwise rectangular cycle on a P–V diagram: pressure between 1 × 10⁵ Pa and 3 × 10⁵ Pa, and volume between 2 L and 5 L. The net work done by the gas per cycle is:
Q17. One mole of an ideal gas expands isothermally at 300 K until its volume doubles (R = 8.31 J mol⁻¹ K⁻¹, ln 2 = 0.693). The work done by the gas is:
Q18. A monatomic ideal gas (γ = 5/3) at 300 K is compressed adiabatically and reversibly to one-eighth of its volume. Its final temperature is:
Q19. The amount of heat needed to raise the temperature of 2 mol of a diatomic ideal gas (rotation active, no vibration) by 20 K at constant volume is (R = 8.31 J mol⁻¹ K⁻¹):
Q20. Hydrogen (molar mass 2 g mol⁻¹) and oxygen (molar mass 32 g mol⁻¹) gases are at the same temperature. The ratio of the rms speed of oxygen molecules to that of hydrogen molecules is:
Q21. An ideal gas in an insulated container expands freely into an evacuated, insulated, rigid chamber, doubling its volume. The gas temperature:
Q22. A bubble rises from the bottom of a lake 20 m deep to the surface at constant temperature. Take atmospheric pressure as equivalent to 10 m of water. The ratio of its final volume to initial volume is:
Q23. A Carnot engine works between a source at 400 K and a sink at 300 K. The sink temperature is lowered by 100 K without changing the source. The new efficiency is:
Q24. A Carnot refrigerator keeps its freezer at −3 °C in a room at 27 °C. The work needed to remove 900 J of heat from the freezer is:
Q25. The latent heat of fusion of ice is 3.3 × 10⁵ J kg⁻¹. When 2 kg of ice melts at 0 °C, the change in entropy of the ice–water system is about:
Q26. 600 J of heat flows directly from a large reservoir at 400 K to another large reservoir at 300 K. The net change of entropy of the two reservoirs is:
Q27. Four engines each absorb 1000 J of heat per cycle from a reservoir at 500 K and reject heat to a reservoir at 300 K. Which engine, with the stated work output per cycle, is impossible?
Q28. An engine of 25 % efficiency delivers 12 kW of mechanical power. The fuel releases 4 × 10⁷ J kg⁻¹ on burning. The fuel consumption rate is:
Q29. Through the same point on a P–V diagram, an adiabatic curve and an isothermal curve are drawn for an ideal gas of ratio of specific heats γ. The magnitude of the adiabatic slope is larger than that of the isothermal slope by a factor of:
Q30. A gas of density 1.2 kg m⁻³ has an rms molecular speed of 500 m s⁻¹. Using the kinetic theory expression, its pressure is: