UPSC Physics 2021

(a) A particle moving in a central force field describes the path r = ke^αθ, where k and α are constants. If the mass of the particle is m, find the law of force. (10 marks) (b) A…

(a) A body of mass m at rest splits into two masses m₁ and m₂ by an explosion. After the split the bodies move with a total kinetic energy T in opposite direction. Show that their…

(a) In a step-index optical fiber system, explain the terms pulse dispersion and material dispersion. An optical fiber having refractive indices of core and cladding n₁ = 1·463 an…

(a) (i) Define moment of inertia and radius of gyration of a body of mass M rotating about an axis. State and prove Parallel Axis theorem on moment of inertia. (15 marks) (ii) A s…

(a) Given that the electric potential of a system of charges is V = 12/r² + 1/r³ volt. Calculate the electric field vector at the Cartesian point (4, 2, 3) m. (10 marks) (b) Eight…

(a) In an inertial reference frame S there is only a uniform electric field E⃗ = 8 kVm⁻¹. Find the magnitude of E⃗' and B⃗' in the inertial reference frame S' moving with a consta…

(a) A region 1, z < 0, has a dielectric material with εᵣ = 3·2 and a region 2, z > 0 has a dielectric material with εᵣ = 2·0. Let the displacement vector in the region 1 be, D⃗₁ =…

(a) (i) The melting point of tin is 232°C, its latent heat of fusion is 14 cal/g and the specific heat of solid and molten tin are 0·055 and 0·064 cal/g °C respectively. Calculate…

(a) Find the minimum magnetic field needed for the Zeeman effect to be observed in a spectral line of 400 nm wavelength when a spectrometer whose resolution is 0·010 nm is used. W…

(a) Using Pauli spin matrices prove that, (i) σₓσᵧ + σᵧσₓ = 0; σᵧσᵤ + σᵤσᵧ = 0; σₓσᵤ + σᵤσₓ = 0 (ii) σ₊σ₋ = 2(1+σᵤ) (iii) σₐ + σᵦ = iσᵧ where α ≠ β ≠ γ 8+6+6 marks (b) Find the un…

(a) In observing the Raman spectrum of a sample using 3637Å as the exciting line, one gets stoke line at 3980Å. Deduce the Raman shift in m⁻¹ units. Compute the wavelength in Å fo…

(a) A particle of rest mass m₀ has a kinetic energy K, show that its de Broglie wavelength is given by λ = hc/√[K(K+2m₀c²)] Hence calculate the wavelength of an electron of kineti…

(a) An X-ray beam of wavelength (λ₁) undergoes a first order Bragg reflection at a Bragg angle of 30°. X-ray of wavelength 97 nm undergoes 3rd order reflection at a Bragg angle of…

(a) What is the importance of study of deuteron ? Obtain the solution of Schrödinger equation for ground state of deuteron and show that deuteron is a loosely bound system. (20 ma…

(a) An n-p-n transistor with β = 49 is used in common-emitter amplifier mode with Vcc = 10V and RL = 2 kΩ. If a 100 kΩ resistor is connected between the collector and the base of…

(a) Sketch the dc load line for the circuit shown. (10 marks) (b) A solid contains a dilute concentration of Nd³⁺ ions, each of which possess three 4f electrons. Assuming that the…