UPSC Physics 2022

An electron is moving under the influence of a point nucleus of atomic number Z. Show that the orbit of the electron is an ellipse. 10 marks Show that the mean kinetic and potenti…

Consider two frames of reference S and S' having a common origin O. The frame S' is rotating with respect to the fixed frame S with a uniform ω⃗ = 3aₓ rad s⁻¹. A projectile of uni…

(a) A homogeneous right triangular pyramid with the base side a and height 3a/2 is shown below. Obtain the moment of inertia tensor of the pyramid : 20 marks (b) Newton's rings ar…

(a) Consider the diagram below with a water flow rate Q. Derive the expression for Q in terms of the difference in the manometer heights h and the cross-section areas A₁ and A₂ :…

(a) Assume that the Earth's atmosphere is pure nitrogen in thermodynamic equilibrium at a temperature of 300 K. Calculate the height above sea level at which the density of the at…

(a) Write down Maxwell's equations in a non-conducting medium with constant permeability and susceptibility (ρ = j = 0). Show that E⃗ and B⃗ each satisfies the wave equation, and…

(a) A metal guitar string with a length of 70 cm vibrates at its fundamental frequency of 246.94 Hz in a uniform magnetic field of 10 T oriented perpendicular to the plane of vibr…

(a) In a partially conducting medium, εᵣ = 18.5, μᵣ = 800 and σ = 1 S m⁻¹. Find α, β, η and the velocity u, for a frequency of 10⁹ Hz. Determine H⃗(z, t). Given, E⃗(z, t) = 50 e⁻α…

(a) What is de Broglie concept of matter wave ? Evaluate de Broglie wavelength of Helium that is accelerated through 300 V. (Given mass of proton = Mass of neutron = 1·67×10⁻²⁷ kg…

(a) Set up the Schrodinger's wave equation for one dimensional potential barrier and obtain the probability of tunneling. 20 marks (b) Show that Eₙ = <V> in the stationary states…

(a) What is the spin wave function (for s=1/2) if the spin component in the direction of unit vector η has a value of 1/2ℏ ? 15 marks (b) (i) Why does Stern-Gerlach experiment enj…

(a) (i) In a diatomic molecule when one constituent atom is replaced by one of its heavier isotopes, what change takes place in the rotational spectrum ? (ii) Calculate the change…

(a) If the nuclear force is charge independent and a neutron and proton form a bound state then why is there no bound state for two neutrons ? What information does this provide o…

(a) Show that for a specific value (n, l), there exists a large degeneracy relative to the energy characterized by the quantum number (N). Find the shell closures and the magic nu…

(a) Explain the drawbacks of Einstein's theory of specific heat and how it was overcome by Debye. 20 marks (b) A neutron and a proton can undergo radiative capture at rest: n + p…

(a) Show that for an n-type semiconductor, the Fermi level lies midway between the donor states and the conduction band edge at low temperature (assuming Eᵥ = 0). 20 marks (b) The…