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.2.
(a) What is Gradient of a scalar function? Give its physical significance and show that Grad φ = ∇φ. (10)
(b) Define the term “acceleration” and find its Cartesian components. (06)
(c) If A = xz³i − 2x²zj + 2yz⁴k, then find curl of A at the point (1, −1, 1). (04)
Total: (20)
Q.3.
(a) Explain the rotational kinetic energy and determine its formula for a disc, hoop and sphere. (10)
(b) What do you mean by the term “inertia” in physics? Calculate respectively the rotational inertia of a solid cylinder and a hollow cylinder about an axis of symmetry. (06)
(c) Calculate the angular speed of the second hand, minute hand and hour hand of a watch. (04)
Total: (20)
Q.4.
(a) What was Physics like before relativity and how did Einstein come up with his theory? Mathematically explain how mass and energy are interchangeable. (10)
(b) Discuss in detail the relativity of length using Einstein’s special theory of relativity. (06)
(c) Calculate the mass equivalent of energy from an antenna radiating 10 kW for 24 hours. (04)
Total: (20)
Q.5.
(a) Define capillarity and derive an expression for the rise of liquid in a capillary tube to show that the height of the liquid column supported is inversely proportional to the radius of the tube. (10)
(b) What are fluids? Write their important characteristics. (06)
(c) A cylindrical swimming pool has radius 2 m and depth 1.3 m. It is filled completely with salt water.
Given:
Density of salt water = 1.03 × 10³ kg m⁻³
Volume of water = 16.34 m³
Atmospheric pressure = 1.013 × 10⁵ Pa
Calculate the pressure at the bottom of the pool. (04)
Total: (20)
Q.6.
(a) For a wave travelling through a medium, demonstrate that the total energy per unit volume is always equal to one half the kinetic energy and one half the potential energy. (10)
(b) The longitudinal waves can pass through solids. How is it possible and on what parameters does the velocity of such waves depend? (06)
(c) The angular vibrational frequency of a CO molecule is 0.6 × 10¹⁵ s⁻¹. Calculate the amount of work required for stretching it by 0.5 Å from the equilibrium position. (04)
Total: (20)
Q.7.
(a) An ideal gas is enclosed in a cylinder with a movable piston. Calculate the work done on such gas and show that pressure force is non-conservative. (10)
(b) State and briefly explain the intermolecular forces. (06)
(c) Oxygen gas having a volume of 1130 cm³ at 42°C and a pressure of 101 kPa expands until its volume becomes 1530 cm³ and its pressure becomes 106 kPa. Find the number of moles of oxygen in the system and its final temperature. (04)
Total: (20)
Q.8.
Write short notes on ANY TWO:
(a) Kepler’s Law of Periods
(b) Michelson Interferometer
(c) Young’s Double Slit Experiment
PAPER-II (Subjective) 80 Marks
PART-II
Attempt ONLY FOUR questions from PART-II, ALL Questions carry EQUAL marks.
Q.2.
A particle of mass m is in the state:
ψ(x,t) = A e^−a[(mx²/h) + it]
where A and a are positive constants.
(a) Find A. (05)
(b) For what potential energy function V(x) does ψ(x,t) satisfy the Schrödinger equation? (05)
(c) Calculate the expectation values of x, x², p and p². (05)
(d) Find σx and σp. Is their product consistent with the uncertainty principle? (05)
Total: (20)
Q.3.
(a) Consider a pair of copper wires 1 mm in diameter and 5 cm apart. In copper the number of conduction electrons per cubic meter is 8.45 × 10²⁸. Suppose their mean drift velocity is 0.3 cm/s. Calculate the current in each wire. (08)
(b) If the wires are 20 cm apart, calculate the magnetic force on the wires. (08)
(c) Define electric current in a wire with respect to the number of charges and their drift velocity. (04)
Total: (20)
Q.4.
Give expressions for the following quantities in terms of e, h, c, k, me and mp.
(a) The energy needed to ionize a hydrogen atom. (05)
(b) The difference in frequency of the Lyman-α line in hydrogen and deuterium atoms. (05)
(c) The magnetic moment of the electron. (05)
(d) The spread in measurement of the π⁰ mass, given that the π⁰ lifetime is τ. (05)
Total: (20)
Q.5.
(a) An atom is capable of existing in two states: a ground state of mass M and an excited state of mass M + Δ. If the transition from ground to excited state proceeds by absorption of a photon, what must be the photon frequency in the laboratory where the atom is initially at rest? (07)
(b) Derive the energy levels of the hydrogen atom from Coulomb’s law and the simple quantization of angular momentum. (07)
(c) In radio astronomy, hydrogen atoms are observed in which radiative transitions from n = 109 to n = 108 occur. What are the frequency and wavelength of the radiation emitted in this transition? (06)
Total: (20)
Q.6.
(a) Consider the elastic vibrations of a crystal with one atom in the primitive cell and calculate the frequency of an elastic wave in terms of the wave vector that describes the wave and in terms of the elastic constants. (12)
(b) Describe vibrations of crystal. (08)
Total: (20)
Q.7.
(a) Discuss density of states in three dimensions. (08)
(b) Describe Debye model for density of states. (08)
(c) Define phonon heat capacity. (04)
Total: (20)
Q.8.
Write notes on ANY TWO:
(a) Maxwell’s Equations
(b) Magnetic Materials (Ferromagnetic, Diamagnetic, Paramagnetic)
(c) Black Body Radiation
×