UPSC Physics 2024

(a) A particle of mass m kg having an initial velocity V₀ is subjected to a retarding force proportional to its instantaneous velocity. Obtain the expression for the velocity and…

(a) (i) Briefly discuss the Kepler's laws of planetary motion. 5 marks (ii) Show that the escape velocity V_e on the surface of the Earth is given by V_e = √(2gR), where g = 9·8 m…

(a) (i) Explain the phenomenon of double refraction. What are positive and negative crystals? Give their examples. (5 marks) (ii) What do you understand by optical activity? A lin…

(a) (i) Write down the system matrix for a combination of two thin lenses in paraxial approximation. Hence obtain the focal length of the combination and the positions of unit pla…

(a) In spherical coordinates, V = –25 V on a conductor at r = 2 cm and V = 150 V on another conductor at r = 35 cm. The space between the conductors is a dielectric for which εᵣ =…

(a) Using Maxwell's equations, obtain Poisson's equation and Laplace's equation. The region -(π)/2 < z/(z₀) < (π)/2 has a charge density ρ = 10⁻⁸ cos(z/(z₀)) (C/m³). Elsewhere the…

(a) How does Planck's law resolve the ultraviolet catastrophe predicted by classical physics? Calculate the average energy ε̄ of an oscillator of frequency 0·60×10¹⁴ s⁻¹ at T = 18…

(a) (i) Explain the T-s diagram for the reversible Carnot cycle and hence obtain the expression for the efficiency of the Carnot engine. (10 marks) (ii) The specific heat of a sol…

Q1. (a) A particle limited to the x-axis has the wave function φ(x) = bx² between x = 0 and x = 2; the wave function φ(x) = 0 elsewhere. (i) Find the probability that the particle…

Q2. (a) Prove that : (i) [L², Lz] = 0 (ii) [Lz, L+] = ℏL+ (iii) [L+, L-] = 2ℏLz (iv) L+ L- = L² - Lz² + ℏLz where ℏ = h/2π (ℏ is Planck's constant) 5+5+5+5=20 marks (b) The ground…

(a) How do Stokes lines appear in Raman spectrum as per classical and quantum theory of Raman effect ? 20 marks (b) What is Lamb shift in the fine structure of hydrogen spectrum ?…

(a) (i) Using free electron theory of metals, calculate the Fermi energy level of sodium atom at absolute zero. Assume that sodium has one free electron per atom and its density i…

(a) Compare nuclear density of hydrogen (₁H¹) with its atomic density. (Assume the atom to have the radius of its first Bohr orbit). What inference can one get from the above comp…

(a) Does the nucleus possess magnetic moment ? Justify your answer. Define nuclear magneton (μN) and Bohr magneton (μB). Calculate their values. 7+8=15 (b) (i) Write semi-empirica…

(a) Discuss the distribution and characteristics of the black soil in India. 10 (b) Examine the role of rivers in the economic development of India. 10

(a) Discuss the factors responsible for the uneven distribution of population in India. 10 (b) Analyse the impact of globalization on the Indian economy. 10