UPSC Physics Optional PYQs (CSE & IFoS)PYQs

A particle of mass m, with energy E such that -V_0 < E < 0, is trapped in a potential wall as shown below :

Write time independent Schrodinger equation in regions (i) 0 < x < a and (ii) x > a.

Obtain an expression from which the energy eigen values can be determined.

Show that for at least one bound state to exist. a^2 V_0 \ge \frac{h^2 \pi^2}{8m}

(i) Explain what do you understand by Heisenberg uncertainty principle. Using this principle, determine the energy of the ground state of a one dimensional simple harmonic oscillator. (ii) An electron having an energy 2 eV is travelling in the region where V(x) varies as shown below:

Calculate the de Broglie wavelength of the electron in regions I, II and III.

Number at non-interacting electrons are confined in a cube of volume L^3. Obtain an expression for the Fermi energy.

100 particles at a temperature T and distributed among three energy levels E_0 = 0, E_1 = kT and E_2 = 2kT. What is the total energy of the system ?

Two bodies A and B have the same mass m each and are made of the same material with specific heat C per unit mass. A is at a temperature T and B is at a temperature 4T. What will be the entropy change of the universe when the bodies are brought into diathermic contact with each other?

Define Fermi energy. For an ideal Fermi gas of N particles at absolute zero temperature, show that the total energy of is 3/5 N E_F, where E_F is the Fermi energy.

Describe the Otto cycle and obtain an expression for the efficiency of the cycle, Show that the efficiency is lower than that of a Carnot cycle operating between the highest and the lowest temperature of Otto cycle.

Consider an infinite grounded conducting plane. If a point charge is held at a distanced d from the plane, compute by method of images, the electric potential above the plane and the induced charges on the conductor.

A bridge network with resistance, capacitance and inductance is given in the above figure. Show that the conditions for balancing the bridge are independent of the frequency of applied voltage.

Show that a sprining nucleus precesses in a magnetic field. Explain the underlying principle of NMR spectroscopy. The magnetic moment of a position is 2.793 \mu\text{ N}. Calculate the radio frequency at which nuclear magnetic resonance occurs in water kept in a magnetic field of T.

Earth receives 1.3\text{KW/m}^2 of radiant energy from the Sun. Assuming Sun to be a spherical black body of radius 7 \times 10^8\text{m} and Earth-sun distance to be 1.5 \times 10^{11}\text{m}, Calculate the surface temperature of Sun. (Stefan-Boltzmenn constant \sigma = 5.67 \times 10^{-8}\text{ Wm}^{-2}\text{K}^{-4}).

A plane wave of frequency \omega, which into two linear dielectric media. It has a normal incidence at the interface of the media. Giving appropriate for the intensities of reflected and transmitted rays.

Define Poynting vector and explain its significance. The electric field vector for an electromagnetic field travelling in vacuum is given by \vec{E} = E_0 \cos (kz - \omega t) \hat{i} Calculate the Poynting vector for the wave and show that its magnitude is equal to the energy density of the wave time the velocity of light.

A parallel LC circuit is operated at a frequency \omega, which is less than the resonant frequency \omega_0 of the LC circuit. Explain whether the reactance is inductive or capacitive.

What is Laplace equation ? Determine the average electric potential over a spherical surface, due to a point charge q placed at a distance r from the centre of the sphere. Assume r to be greater than the radius of the sphere.

A cylinder of length L and radius b has its axis coincident with z-axis. The electric held in th region is E = 100 k. Find the electric flux through (i) the top circular end (ii) the bottom circular end (iii) the curved wall of the cylinder (iv) the closed surface of the cylinder

Two thin convex lenses of focal length 0.2 m and 0.1 m are located 0.1m apart on the axis of symmetry. An object of height 0.1m is placed at a distance of 0.2 m from the first lens. Find by the matrix method, the position and the height of the image.

What is holography ? Describe the experimental set up for Gabor's on-line holographic recording. What are the limitations of Gabors experiments? How these were over come by Leith and Upatneiks?