Federal Public Service Commission (FPSC)
Competitive Examination for Recruitment to BPS-17 Posts under the Federal Government
Paper: Physics
Time Allowed: 3 Hours
PAPER-I (Subjective) 80 Marks
PART-II
Attempt ONLY FOUR questions from PART-II, ALL Questions carry EQUAL marks.
Q. No. 2
(a) State and prove Stoke’s theorem.
(b) Prove that if the vector is the gradient of a scalar function, then its line integral around a closed curve is zero.
(c) A particle moves along the curve:
x = 2t²,
y = t² − 4t,
z = 3t − 5,
where t is the time. Find the components of its velocity and acceleration at time t = 1 in the direction 2i − 3j + 2k.
Q. No. 3.
(a) What is moment of inertia? State and prove the parallel axis theorem.
(b) Calculate the rotational inertia of a hollow cylinder about its cylindrical axis.
Q. No. 4.
(a) State and prove Kepler’s law of areas and Kepler’s law of periods of planetary motion.
(b) A satellite orbits at a height of 230 km above the Earth’s surface. What is the period of the satellite?
(c) At what altitude above the Earth’s surface is the value of g equal to three-quarters of its value at the Earth’s surface?
Q. No. 5.
(a) What is a diffraction grating? Explain how a grating diffracts light. Derive the relation for the resolving power of a grating.
(b) What is meant by polarization of light? How can plane-polarized light be obtained by using a polarizing sheet?
Q. No. 6.
(a) Derive the Lorentz velocity transformation equations and show that the speed of light is independent of the relative motion between the frames of reference.
(b) The siren of a police car emits a source tone at a frequency of 1125 Hz. Find the frequency received in your car under the following circumstances:
(i) Your car is at rest, and the police car is moving towards you at 29 m/s.
(ii) The police car is at rest, and your car is moving towards it at 29 m/s.
(iii) Both your car and the police car are moving towards one another at 14.5 m/s.
(iv) Your car is moving at 9 m/s, and the police car is chasing behind you at 38 m/s.
Q. No. 7.
(a) Define entropy. State the Second Law of Thermodynamics in terms of entropy.
(b) Discuss the applications of the First Law of Thermodynamics.
(c) Discuss briefly the Lissajous patterns.
Q. No. 8.
Explain any FOUR of the following:
(a) Doppler’s Effect
(b) Bernoulli’s Theorem
(c) Newton’s Rings
(d) He-Ne Gas LASER
(e) Brownian Motion
PAPER-II (Subjective) 80 Marks
PART-II
Attempt ONLY FOUR questions from PART-II, ALL Questions carry EQUAL marks.
Q. No. 2
(a) Define electric field intensity E⃗. State its value for a point charge and give its units. (8)
(b) State differential form of Gauss’s law and from there develop the Poisson’s and Laplace’s equations. (8)
(c) A charge of 10√2 Coulomb is located at (3î + 4ĵ + 5k̂) m. Calculate the electric field intensity at a point having position vector (5î + 4ĵ + 3k̂) m. (4)
Q. No. 3.
(a) Differentiate between a series and parallel resonant circuits. (6)
(b) Explain the construction and operation of a transformer. What are energy losses in a transformer and how are they reduced to a minimum. (10)
(c) A series LCR circuit contains a coil with L = 2.25 H, a capacitor having C = 16 μF and a resistor with R = 50 Ω. Calculate the impedance and the phase difference between current and voltage. (Take frequency f = 50 Hz) (4)
Q. No. 4.
(a) State and explain the basic postulates of Quantum Physics. (5)
(b) Briefly explain with examples what do you mean by Eigen function and Eigen values. (5)
(c) Derive the time-dependent Schrödinger Wave Equation for a free particle. (10)
Q. No. 5.
(a) Why does the resistivity of metals increase with temperature but that of semiconductors decrease? (6)
(b) In the process of making semiconductor devices, why is silicon preferred over germanium? (4)
(c) Briefly explain the construction and operation of a Bipolar Junction Transistor (BJT). How can it be used as an amplifier? (10)
Q. No. 6.
(a) What do <111>, [010], (111), and {100} represent for a cubic crystal lattice? (5)
(b) What is packing factor? Determine the Atomic Packing Factor of FCC lattice. (5)
(c) With a neat diagram showing X-ray diffraction, derive an expression for Bragg’s Law. (10)
Q. No. 7.
(a) Define Curie and Becquerel. Establish the relation between them. (6)
(b) Calculate the decay constant for ¹⁴C which has a half-life of 5730 years. (4)
(c) State and explain Half-life and Mean life of a radioactive element. Show that <T> is greater than T₁⁄₂. (10)
Q. No. 8.
Write comprehensive notes on any TWO of the following: (10 each)
(a) Semiconductor Laser (LASER)
(b) Hall Effect
(c) Scintillation Counter
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