UPSC Physics 2023

(a) A force F⃗ is given by F⃗ = x²y x̂ + zy² ŷ + xz² ẑ. Determine whether or not the force is conservative. 10 marks (b) Calculate the gravitational self-energy of the Earth. Gi…

(a) (i) Derive the expressions for gravitational potentials at a point (I) outside the spherical shell, (II) inside the spherical shell. 10 marks (ii) Calculate the escape velocit…

(a) (i) What are the requisite conditions for observation of interference pattern on a screen ? (5 marks) (ii) Derive the expression for fringe width and intensity at a point on t…

(a) Write conditions for working of a step-index optical fiber. In a step-index fiber, the core and cladding materials have refractive indices 1·50 and 1·43, respectively. Find th…

(a) Find the energy stored in a system of four charges Q₁ = 1 nC, Q₂ = 2 nC, Q₃ = 3 nC and Q₄ = 4 nC placed at the cartesian coordinates R₁(1, 1), R₂(2, 1), R₃(1, 4) and R₄(2, 2),…

(a) Two inductors having inductances L₁ and L₂ are connected in parallel. The inductors have a mutual inductance M. Derive the expression for the effective inductance. Assume the…

(a) A neutral atom consists of a point nucleus +q surrounded by a uniformly charged spherical cloud (-q) of radius r. Show that when such an atom is placed in a weak external elec…

(a) A circular ring of radius R lying on the x-y plane and centred at the origin, carries a uniform line charge λ. Find the first three terms (monopole, dipole and quadrupole) of…

(a) Calculate the zero point energy for a particle in an infinite potential well for the following cases : (i) a 100 g ball confined on a 5 m long line. (ii) an oxygen atom confin…

(a) An operator P describing the interaction of two spin 1/2 particles is P = a + bσ⃗₁·σ⃗₂, where a and b are constants, and σ⃗₁ and σ⃗₂ are Pauli matrices of the two spins. The t…

(a) What is vector atom model ? How the principal features of vector atom model were explained by Stern-Gerlach experiment ? (5+10=15 marks) (b) What is Lande's g factor ? Evaluat…

(a) A particle constrained to move along x-axis in the domain 0 ≤ x ≤ L has a wave function ψ(x) = sin(nπx/L), where n is an integer. Normalize the wave function and evaluate the…

(a) How could you establish that νₑ and ν̄ₑ are two different particles ? 10 marks (b) What is the age of a fossil that contains 6 g of carbon ¹⁴C and has a decay rate of 27 decay…

(a) Establish the Rutherford's scattering cross section formula for α-particle by considering the standard assumptions and symbols. 20 marks (b) By assuming the nucleus as a cubic…

(a) Explain classical theory of diamagnetism. Show that the susceptibility of diamagnetic substances is directly proportional to the atomic number. Why all the electrons in an ato…

(a) What do you understand by the critical size of a reactor ? Explain the main features of nuclear reactors. 5+15=20 (b) What is superconductivity ? Explain Meissner effect. Why…