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 (Objective) 20 Marks
PART-I
Q. No. 1.
Select the best option/answer and fill in the appropriate box on the Answer Sheet.
(i) A body is moving northward and the force applied is eastward. The acceleration produced is:
(a) Northward
(b) At 45° East of North
(c) Eastward
(d) None of these
(ii) The correct dimensions of power are:
(a) [ML²T⁻³]
(b) [ML³T⁻²]
(c) [ML²T⁻⁴]
(d) None of these
(iii) The work done by the force
F = (4ax − 3ay − 2az) N
in giving a 1 nC charge a displacement
r = (10ax + 2ay − 7az) m
is:
(a) 10 nJ
(b) 15 nJ
(c) 20 nJ
(d) None of these
(iv) Three masses are placed on the x-axis: 200 g at x = 0, 500 g at x = 30 cm, and 400 g at x = 70 cm. The center of mass is:
(a) 0.89 m
(b) 0.69 m
(c) 0.39 m
(d) None of these
(v) A 60 kg woman stands on a light cubical box having sides of 5.0 cm. The box rests on the floor. What pressure does the box exert on the floor?
(a) 2.4 × 10⁵ N/m²
(b) 5 × 10⁵ N/m²
(c) 3 × 10⁵ N/m²
(d) None of these
(vi) The SI unit of stress is the same as that of:
(a) Force
(b) Momentum
(c) Pressure
(d) None of these
(vii) What is the maximum speed at which a car can round a curve of radius 25 m on a level road if the coefficient of static friction between the tires and the road is 0.80?
(a) 25 m/s
(b) 14 m/s
(c) 10 m/s
(d) None of these
(viii) The equation of simple harmonic motion having amplitude 5 m and time period 0.5 s is:
(a) y = 5 sin(4πt)
(b) y = 0.5 sin(2πt/5)
(c) y = 5 sin(2πt)
(d) None of these
(ix) Two particles, each of mass 5.0 kg, are mounted 4.0 m apart on a massless light rod capable of rotating about its center. The moment of inertia is:
(a) 1.25 kg·m²
(b) 20 kg·m²
(c) 40 kg·m²
(d) None of these
(x) The time period of a 1 kg mass attached to a spring of spring constant 100 N/m is:
(a) 0.2π
(b) π
(c) 2π
(d) None of these
(xi) A 14 cm inner diameter water main supplies water through intermediate pipes to a faucet pipe of 1.00 cm inner diameter. If the average speed in the faucet pipe is 3.0 cm/s, what is the average speed in the water main?
(a) 0.015 cm/s
(b) 0.15 m/s
(c) 0.5 m/s
(d) None of these
(xii) What is the tension T in the rope if a 10 N weight is pulled upward with a constant velocity of 2 m/s?
(a) 12 N
(b) 8 N
(c) 5 N
(d) None of these
(xiii) The ratio of linear stress to linear strain is called:
(a) Young’s Modulus
(b) Bulk Modulus
(c) Deformation
(d) None of these
(xiv) A body is moving with constant speed in a circle. Its velocity vector:
(a) Remains constant
(b) Changes its magnitude
(c) Changes its direction
(d) None of these
(xv) When a constant torque acts on a rotating system, which of the following remains constant?
(a) Angular velocity
(b) Angular acceleration
(c) Angular momentum
(d) None of these
(xvi) A planet has four times the mass and twice the diameter of the Earth. The value of g on the planet is:
(a) 19.6 m/s²
(b) 9.8 m/s²
(c) 4.9 m/s²
(d) None of these
(xvii) A geostationary satellite revolves around the Earth from:
(a) East to West
(b) West to East
(c) North to South
(d) None of these
(xviii) According to Einstein, with a great increase in the speed of a body, the relativistic:
(a) Length remains constant
(b) Time decreases
(c) Mass increases
(d) None of these
(xix) If the graph between 1/m and a is a straight line, then:
(a) m ∝ a
(b) m ∝ 1/a
(c) m ∝ 1/a²
(d) None of these
(xx) The angular frequency (ω) of rotation of a spaceship about its own axis to create gravity equal to that of Earth is:
(a) √(g/r)
(b) √(r²/g)
(c) √(g/r²)
(d) None of these
PAPER-I (Subjective) 80 Marks
PART-II
Attempt ONLY FOUR questions from PART-II, ALL Questions carry EQUAL marks.
Q. No. 2.
(a) Define gradient. Find the gradient of the magnitude of the position vector r. What conclusion do you derive from the result?
(b) Sketch the vector field
V = −yî + xĵ
Find:
(i) Curl V
(ii) Divergence V
Q. No. 3.
(a) What is the Theory of Relativity? Consider two inertial frames A and B with parallel axes and origins O and O′ coinciding at t = t′ = 0. Frame B moves with uniform velocity v along the x-axis of frame A.
Given the Lorentz transformations:
x′ = γ(x − vt)
y′ = y
z′ = z
t′ = γ(t − vx/c²)
where
γ = 1/√(1 − v²/c²)
Using the principle of equivalence of inertial frames, derive the inverse Lorentz transformation (B → A).
(b) One of Maxwell’s equations in inertial frame 1 is:
∇ × B₁ = μ₀ (ε₀ ∂E₁/∂t₁ + J₁)
Write this equation in inertial frame 2 according to Einstein’s principle of relativity. Does B₁ = B₂?
Q. No. 4.
(a) State and prove Bernoulli’s Theorem.
(b) If the speed of airflow past the lower surface of an airplane wing is 110 m/s, what speed of flow over the upper surface will produce a pressure difference of 900 Pa? Take the density of air as 1.3 × 10⁻³ g/cm³.
Q. No. 5.
(a) Describe waves and their types. Derive the expression for the speed of a wave on a stretched string using Newton’s Second Law.
(b) The equation of a transverse wave on a string is:
Y = (2 mm) sin[(20 m⁻¹)x − (600 s⁻¹)t]
The tension in the string is 15 N.
(i) Find the wave speed.
(ii) Find the linear density of the string in g/m.
Q. No. 6.
(a) What is interference of waves? State the conditions for constructive and destructive interference. Explain the working of any one interferometer.
(b) Two coherent sound waves of frequency 450 Hz travel in the same direction with a speed of 330 m/s. Find the phase difference at a point that is 4.4 m from one source and 4.0 m from the other source.
Q. No. 7.
(a) State and explain the Second Law of Thermodynamics. Prove that the Clausius and Kelvin–Planck statements are equivalent.
(b) A Carnot engine operates between temperatures of 850 K and 300 K. The engine performs 1200 J of work in each cycle, and each cycle takes 0.25 s.
Calculate:
(i) Efficiency
(ii) Average power
(iii) Heat input per cycle
(iv) Heat rejected per cycle
Q. No. 8.
Write short notes on ANY TWO of the following:
(i) Laser and its applications
(ii) Classical Maxwell–Boltzmann Statistics
(iii) Dynamics of Rigid Bodies
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PAPER-II (Objective) 20 Marks
PART-I
Q. No. 1.
Select the best option/answer and fill in the appropriate box on the Answer Sheet.
(i) The impedance of a series RLC circuit at resonance is:
(a) Greater than R
(b) Equal to R
(c) Zero
(d) None of these
(ii) An electron has a velocity of 10 km/s perpendicular to a magnetic field of flux density 0.1 T. If the radius of its path is 569 nm, the frequency is:
(a) 2.79 GHz
(b) 3.1 MHz
(c) 2.8 kHz
(d) None of these
(iii) If a current of 10 A flows through an electric heater for one hour and converts 8.64 MJ of electrical energy into heat, the potential difference across the heater is:
(a) 864 V
(b) 240 V
(c) 100 V
(d) None of these
(iv) An alpha particle is accelerated to a velocity v by a potential difference of 1200 V. What potential difference is required to double its velocity?
(a) 2400 V
(b) 3600 V
(c) 4800 V
(d) None of these
(v) Two thin parallel wires carry currents in the same direction. The force between them is:
(a) Parallel to the wires
(b) Perpendicular to the wires and attractive
(c) Perpendicular to the wires and repulsive
(d) None of these
(vi) If a current of 300 mA passes through an electric bulb, the number of electrons passing through it in one minute is:
(a) 1.12 × 10²⁰
(b) 1.6 × 10¹⁹
(c) 6.02 × 10¹⁸
(d) None of these
(vii) An electric iron of resistance 20 Ω draws a current of 5.0 A. The thermal energy developed in 30 s is:
(a) 15 kJ
(b) 100 J
(c) 10 J
(d) None of these
(viii) An ideal gas has a volume of 1.00 L at 1.00 atm and −20°C. To what pressure must it be subjected to compress it to 0.500 L at 40°C?
(a) 5.2 atm
(b) 2.47 atm
(c) 1.5 atm
(d) None of these
(ix) In Bohr’s model of the atom, the lowest orbit corresponds to:
(a) Maximum energy
(b) Minimum energy
(c) Zero energy
(d) None of these
(x) The diffusion of free electrons across an unbiased p-n junction produces:
(a) Forward bias
(b) Reverse bias
(c) Depletion region
(d) None of these
(xi) A p-n junction under forward bias behaves like a:
(a) Capacitor
(b) Inductor
(c) Insulator
(d) None of these
(xii) The impedance at resonance of a series RLC circuit with L = 15 mH, C = 0.015 F and R = 80 Ω is:
(a) 0 kΩ
(b) 30 Ω
(c) 80 Ω
(d) None of these
(xiii) Weber is the SI unit of:
(a) Magnetic field intensity
(b) Magnetic flux
(c) Magnetic flux density
(d) None of these
(xiv) The magnetic flux through an area A in a uniform magnetic field B is given by:
(a) AB
(b) B · A
(c) A × B
(d) None of these
(xv) In an electric circuit, currents flowing toward a node are 2 A, −3 A and 4 A. The current in the fourth branch is:
(a) 2 A
(b) −3 A
(c) 4 A
(d) None of these
(xvi) With the passage of time, the rate of decay of a radioactive element:
(a) Increases exponentially
(b) Decreases linearly
(c) Becomes zero after two half-lives
(d) None of these
(xvii) Controlled nuclear fission chain reactions take place in a:
(a) Black hole
(b) Star
(c) Nuclear reactor
(d) None of these
(xviii) In the nineteenth century, Faraday and Maxwell unified:
(a) Gravitational and weak forces
(b) Electric and magnetic forces
(c) Weak and strong forces
(d) None of these
(xix) The electromagnetic wave theory of light was proposed by:
(a) Newton
(b) Michelson
(c) Maxwell
(d) None of these
(xx) The concept of field theory was introduced by:
(a) Franklin
(b) Kepler
(c) Oersted
(d) None of these
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PAPER-II (Subjective) 80 Marks
PART-II
Attempt ONLY FOUR questions from PART-II, ALL Questions carry EQUAL marks.
Q. No. 2.
Q. No. 2.
(a) State and prove Gauss’s Law. Compare it with Coulomb’s Law for calculating the electric field.
(b) Determine the electric field produced by a spherical cloud of electrons having volume charge density
ρ = ρ₀, for 0 ≤ r ≤ b
and
ρ = 0, for r > b,
where ρ₀ and b are positive constants.
Sketch the charge distribution and the corresponding electric field.
Q. No. 3.
(a) Explain Maxwell’s equations. Write the basic relations for electrostatic and magnetostatic fields. Show how these relations were modified into Maxwell’s equations. What was Maxwell’s main contribution in this regard?
(b) Derive Maxwell’s two divergence equations from the two curl equations and the equation of continuity.
Q. No. 4.
(a) What are P-type and N-type semiconductors? Draw the V-I characteristic of a PN junction. Why does the small reverse saturation current increase suddenly at the breakdown voltage? State the uses of a Zener diode.
(b) What is a transistor? Draw the three common transistor configurations. Explain the operation of a transistor in saturation mode.
Q. No. 5.
What is the Compton Effect? Derive the expression for Compton shift. Explain how it depends upon the scattering angle. What is meant by Red Shift?
Q. No. 6.
(a) Describe Schrödinger’s wave equation. Normalize the wave function
Ψ(x) = Ae^(−αx²)
where A and α are real constants, A has units of (length)⁻¹ᐟ² and α has units of (length)⁻².
(b) Find the probability of locating the particle between x = 0.99 and x = 1.01. Also determine the possible values of E and V.
Given:
∫₋∞^∞ e^(−x²/2) dx = √(2π)
Q. No. 7.
(a) Explain radioactive decay. Derive the expression for the decay rate. Relate half-life to the decay constant. State the units used to measure radioactivity.
(b) A 2.71 g sample of radioactive KCl decays at a constant rate of 440 Bq. The isotope ⁴⁰K constitutes 1.17% of the normal potassium. Calculate the half-life of this nuclide.
Q. No. 8.
Write short notes on ANY TWO of the following:
(i) Poynting Theorem and Poynting Vector
(ii) Elementary Particles and their Properties
(iii) Unification of Forces
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