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Table of Contents
KHYBER PAKHTUNKHWA PUBLIC SERVICE COMMISSION
WRITTEN EXAMINATION FOR THE POSTS OF PMS OFFICER / AETO BPS-17
(2025)
PHYSICS (PAPER-I)
Time Allowed: 03 Hours
Total Marks: 100
Note:- Attempt any five complete questions.
Q.No.1
(a) Define and explain the gradient of a scalar function, and prove that grad S = ∇S.
(10)
(b) If F is a vector, prove that Div. Curl F = 0.
(06)
(c) We know the addition, subtraction, and multiplication of vectors. Why don’t we discuss the division of vectors? Is it possible to define such an operation?
(04)
Q.No.2
(a) Explain relativity of simultaneity.
(06)
(b) Prove the relativistic energy relation E2 = p2c2 + m02c4 where m0 is the rest mass.
(08)
(c) A Tevatron at the Fermi National Accelerator Laboratory accelerates protons to a kinetic energy of about 1 TeV (1012 eV). What is the speed of a proton?
(06)
Q.No.3
(a) State and explain Kepler’s three laws of planetary motion. Show how the third law can be derived from Newton’s law of gravitation.
(10)
(b) A satellite revolves around the Earth in a circular orbit at an altitude of 1000 km above the Earth’s surface. Find the orbital period (T) of the satellite in minutes.
Use: RE = 6.37 × 106 m, ME = 5.97 × 1024 kg, G = 6.67 × 10-11 N.m2/kg2.
Use: RE = 6.37 × 106 m, ME = 5.97 × 1024 kg, G = 6.67 × 10-11 N.m2/kg2.
(06)
(c) Explain why astronauts in an orbiting spacecraft feel weightless, even though they are under the influence of Earth’s gravity.
(04)
Q.No.4
(a) State Simple Harmonic Oscillator. The kinetic energy and potential energy of simple harmonic oscillators is:
E = K + U = ½ mv2 + ½ kx2 where x = A cos (ωt + φ)
Show graphically:
(i) The variations of KE and PE with time
(ii) The variations of KE and PE with displacement x.
(07)
(b) Consider a mass of 0.80kg is attached to a horizontal spring having spring constant k = 180Nm-1. At time t = 0, the mass is observed to be 0.04m from the equilibrium position and is moving away from the equilibrium position with velocity 0.5ms-1.
(07)