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) What is the curl of a vector field? Explain its physical significance.
(b) What is the vector triple product? Show that:
A × (B × C) = (A · C)B − (A · B)C
(c) If
Ø = 2x³y²z⁴
find div (grad Ø).
Q. No. 3.
(a) State and explain Kepler’s law of areas.
(b) A spaceship of mass m = 4.50 × 10³ kg is in a circular Earth orbit of radius
r = 8.00 × 10⁶ m and period T₀ = 118.6 min = 7.119 × 10³ s. A thruster is fired in the forward direction to decrease the speed to 96.0% of the original speed. What is the period T of the resulting elliptical orbit?
(c) Which has the greater magnitude: the angular momentum of the Earth (relative to its center) associated with its rotation about its axis, or the angular momentum of the Earth (relative to the center of its orbit) associated with its orbital motion around the Sun? Explain.
Q. No. 4.
(a) Explain the equivalence of mass and energy.
(b) Explain the two tests of time dilation, namely microscopic and macroscopic clocks.
(c) The mean lifetime of stationary muons is 2.2000 μs. The mean lifetime of high-speed muons in a burst of cosmic rays observed from Earth is 16.000 μs. Calculate, to five significant figures, the speed parameter β of these cosmic-ray muons relative to Earth.
Q. No. 5.
(a) What is viscosity? Explain it in detail. Discuss the effect of temperature on viscosity.
(b) Castor oil, having a density of 0.96 × 10³ kg/m³ at room temperature, is forced through a circular pipe by a pump maintaining a gauge pressure of 950 Pa. The pipe has a diameter of 2.6 cm and a length of 65 cm. Oil emerging from the pipe is collected, and after 90 s a total of 1.23 kg is collected. Calculate the coefficient of viscosity of the castor oil.
(c) A liquid flows through a horizontal pipe of inner radius 2.52 cm. The pipe bends upward through a height of 11.5 m, where it widens and joins another horizontal pipe of inner radius 6.14 cm. What must be the volume flux if the pressure in the two horizontal pipes is the same?
Q. No. 6.
(a) What is a damped harmonic oscillator? Write its equation of motion and obtain its solution.
(b) The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?
(c) An insulating vessel containing 1.8 kg of water is placed on a hot plate. Initially, both the water and the hot plate are at 20°C. The temperature of the hot plate is raised very slowly to 100°C, where the water begins to boil. Calculate the entropy change of the water during this process.
Q. No. 7.
(a) What are travelling waves? Derive the expression for the rate at which energy is transported by a wave travelling along a string.
(b) A string has linear density μ = 525 g/m and is under tension T = 45 N. A sinusoidal wave of frequency 120 Hz and amplitude 8.5 mm travels along the string. At what average rate does the wave transport energy?
(c) Two sinusoidal waves of identical wavelength and amplitude travel in opposite directions along a string with a speed of 10 cm/s. If the time interval between successive instants when the string is flat is 0.50 s, calculate the wavelength of the waves.
Q. No. 8.
(a) Explain the volume and pressure corrections in the ideal gas law as suggested by van der Waals.
(b) For oxygen, the van der Waals coefficients are:
a = 0.138 J·m³/mol²
b = 3.18 × 10⁻⁵ m³/mol
Assume that 1.00 mol of oxygen at T = 50 K is confined to a container of volume 0.0224 m³.
Calculate the pressure according to:
(i) The ideal gas law
(ii) The van der Waals equation
(c) State and explain the Zeroth Law of Thermodynamics.
PAPER-II (Subjective) 80 Marks
PART-II
Attempt ONLY FOUR questions from PART-II, ALL Questions carry EQUAL marks.
Q. No. 2.
(a) Discuss the electric field of point charges, keeping in view the magnitude of force acting on a test charge according to Coulomb’s Law. (8)
(b) Derive Poisson’s equation from Gauss’s Law. Also write the expression for Laplace’s equation. (8)
(c) Find the electric field due to a charge of 2e at a distance of 26.5 × 10⁻¹² m.
(ε₀ = 8.85 × 10⁻¹² C²/N·m² and e = 1.60 × 10⁻¹⁹ C) (4) (20)
Q. No. 3.
(a) Discuss in detail the Energy Transport and the Poynting Vector. (8)
(b) Write the four Maxwell’s Equations in both integral and differential forms. (8)
(c) Explain Vector Potential. (4) (20)
Q. No. 4.
(a) State and explain Heisenberg’s Uncertainty Principle. (8)
(b) Discuss the phenomenon of Barrier Tunneling. (8)
(c) Find the momentum of an electron moving with a speed of 1.88 × 10⁶ m/s, where the mass of the electron is 9.11 × 10⁻³¹ kg. (4) (20)
Q. No. 5.
(a) What do you understand by the term Doping? How can semiconductors be made n-type or p-type by doping? (8)
(b) Discuss in detail the N-P-N and P-N-P transistors. (8)
(c) Explain MOSFET. (4) (20)
Q. No. 6.
(a) Discuss in detail the process of Natural Radioactivity. (8)
(b) Discuss in detail Radioactive Decay. (8)
(c) Find the energy released during the alpha-decay of ²³⁸U. The required atomic masses are:
²³⁸U = 238.050785 u
²³⁴Th = 234.043539 u
⁴He = 4.002603 u (4) (20)
Q. No. 7.
(a) Discuss in detail the phenomenon of Nuclear Fission. (8)
(b) Explain the basic principles of Nuclear Reactors. (8)
(c) Briefly write about the methods of detection of nuclear radiation. (4) (20)
Q. No. 8.
Write notes on any TWO of the following: (10 each)
(a) Dielectric Medium and Electric Polarization
(b) Ampere’s Law
(c) Accelerators
(20)
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