UPSC Physics 2025

(a) Consider a large stationary cylinder of inner radius R. A smaller solid cylinder of radius r rolls without slipping inside the larger cylinder. Determine the equation of motio…

(a) A body moves about a point 'O' under no force, the principal moments of inertia at 'O' being 3A, 5A and 6A. The components of the initial angular velocity about the principal…

(a) Consider a laser system consisting of an active medium placed between a pair of mirrors forming a resonator. Obtain an expression for the threshold population inversion requir…

(a) Consider a thick lens of thickness t made of a material of relative refractive index n. Let R₁ and R₂ be the radii of curvature of its two surfaces. Obtain the system matrix o…

(a) Consider a point charge of 5 nC placed at a distance of 1 m from a perfect conducting plane (z = 0) of infinite extent. Find the electric field at a point (2, 2, 0) m and show…

(a) Consider a long straight wire of length L carrying a current I. Determine the magnetic vector potential A⃗ at a point P located at distance x from the wire. (20 marks) (b) As…

(a) A ternary system consists of three components (A, B and C) in equilibrium with two phases. Determine the number of degrees of freedom using the Gibb's phase rule and discuss t…

(a) (i) In free space, an electric field (E⃗) is given by the following expression : E⃗ = 10 cos (ω t - 100 x)ĵ V/m Find the angular frequency ω and the displacement current. (10…

(a) Explain how the uncertainty in position is different from the uncertainty or inaccuracy of the measuring instruments. 10 marks (b) Determine the ground state energy of an elec…

(a) What is the density of states? For a relativistic particle of rest mass μ, prove that the density of states in the extreme relativistic limit (E ≫ μc²) is g(E) = V/π²ℏ³c³ E² w…

(a) Find out the difference in frequencies of Lyman-alpha line in hydrogen and deuterium atoms. 15 marks (b) The Stern-Gerlach experiment is a landmark experiment in quantum mecha…

(a) State how for spin-half particles, the spin (σ) can be expressed by its three components σ_x, σ_y and σ_z. 20 marks (b) By applying the Schrödinger's equation to the ground st…

(a) Show that the energy of the triplet state (S = 1) is not equal to the energy of the singlet state (S = 0). 10 marks (b) ρ⁰ and K⁰ mesons both decay mostly to π⁺ and π⁻. Why th…

(a) The total binding energies of ¹⁵₈O, ¹⁶₈O and ¹⁷₈O are 111·96 MeV, 127·62 MeV and 131·76 MeV respectively. Determine the energy gap between 1p₁/₂ and 1d₅/₂ neutron shells for t…

(a) What is the minimum energy required to break a ₂He⁴ nucleus into free protons and neutrons? [ Given, m_H = 1·007825 amu, m_n = 1·008665 amu, m_e = 0·00055 amu and m_He = 4·002…

(a) Classify diamagnetic, paramagnetic and ferromagnetic materials in terms of their magnetic susceptibility (χ). Plot and explain the variation of 1/χ with temperature for the th…