Physics UPSC PYQ 2016

Show that the displacement current between the plates of a parallel-plate capacitor is equal to the conduction current across the conductor.

The primitive translation vectors of a two-dimensional lattice are a = 2i_hat + j_hat, b = 2j_hat. Determine the primitive translation vectors of its reciprocal lattice.

Write down the quark structure of the following hadrons : Delta^++, Omega^-, Sigma^- and Lambda^0. Write down the following decays in terms of quarks : (i) n -> p^+ + e^- + bar_nu_e (ii) Delta^+ -> pi^+ + n (iii) Sigma^+ -> p^+ + pi^0

What do you understand by the term 'phase transition'? Using Clausius-Clapeyron equation, show that for first-order phase transitions, vapour pressure decreases exponentially with temperature. You can assume that the vapour behaves like an ideal gas and latent heat remains constant with temperature.

Why are NAND and NOR gates called universal gates ? Give the logic diagram, Boolean equation and the truth table of a NAND gate.

Explain the various leptonic family members. What is leptonic number conservation ? Based on this conservation law, state whether the following reactions are possible or not : (i) pi^- -> mu^- + bar_nu_tau (ii) n -> p^+ + e^- + bar_nu_e

A typical atomic radius is about 5 x 10^-15 m and the energy of beta-particle emitted from a nucleus is at most of the order of 1 MeV. Prove on the basis of uncertainty principle that the electrons are not present in nuclei.

A student is working in a physics laboratory, which is at temperature 27 degrees C, on a sonometer to study formation of stationary waves. The cross-sectional area of the sonometer wire is 0.85 x 10^-6 m^2 and a tension of 20 N is applied on it. If the rigid supports are 1.2 m apart and the temperature of the wire drops by 7 degrees C, calculate the (i) final tension and (ii) fundamental frequency of vibration of the wire. Take, coefficient of linear expansion and isothermal Young's modulus as 1.5 x 10^-5 K^-1 and 2.0 x 10^11 N m^-2 respectively.

The refractive indices of core and cladding in a step index optical fiber are 1.52 and 1.48 respectively. The diameter of the core is 30 micrometer. If the operating wavelength is 1.3 micrometer, calculate the V parameter and the maximum number of modes supported by the fiber.

Write down van der Waals' equation of state for n moles of a gas and calculate the temperature at which 5 moles of the gas at 5 atm pressure will occupy a volume of 20 litres. Given, R = 8.31 x 10^7 erg mol^-1 K^-1, a = 1.34 x 10^12 dyne cm^4 mol^-2, b = 31.2 cm^3 mol^-1 and 1 atm = 1.013 x 10^6 dyne cm^-2.

Describe Stern-Gerlach experiment. Discuss how it has explained space quantization and electron spin. Find the value of angle between the spin angular momentum S vector and its z-component of an electron moving along the external magnetic field B vector.

State and prove Poynting's theorem.

Can D1 and D2 lines of sodium light (lambda_1 = 5890 Angstrom and lambda_2 = 5896 Angstrom) be resolved in second-order spectrum if the number of lines in the given grating is 450? Explain.

What is Raman effect ? Describe briefly the chief characteristics of pure rotational spectra. The small rotational Raman displacement for HCl molecule is 41.6 cm^-1. Find the internuclear distance between the atoms forming the molecule.

Compute the allowed spectral terms for two non-equivalent p-electrons on the basis of Pauli's exclusion principle.

Using uncertainty principle, calculate the size and energy of the ground state of hydrogen atom.

Obtain an expression for the resolving power of a grating explaining the Rayleigh's criterion of resolution.

A parallel-plate capacitor is connected to a 240 V AC supply having angular frequency of 300 rad/s. Find the r.m.s. value of the conduction current in the circuit. What is the displacement current between the plates of the capacitor? Given, C = 200 pF.

State the basic assumption of single particle shell model. How do the centrifugal and spin-orbit terms remove the degeneracy of a three-dimensional spherical harmonic oscillator ?

Obtain the conditions for constructive interference and destructive interference in a thin film due to reflected light.

Consider a system of N particles and a phase space consisting of only two states with energies 0 and epsilon (> 0). Obtain the expressions for the partition function and the internal energy of the system, if it obeys M-B statistics.

(i) The distance between the centres of the carbon and oxygen atoms in the carbon monoxide (CO) gas molecule is 1.130 x 10^-10 m. Locate the centre of mass of the molecule relative to the carbon atom. (ii) Find the centre of mass of a homogeneous semicircular plate of radius a.

Predict the spin and parity of ground states of the following nuclei on the basis of shell model : (i) 8O^15 (ii) 8O^16 (iii) 17Cl^38

Explain in detail L-S coupling and j-j coupling schemes.

Write down the matrix representation of the three Pauli matrices sigma_x, sigma_y and sigma_z. Prove that these matrices satisfy the following identities: (i) [sigma_x, sigma_y] = 2 i sigma_z (ii) [sigma_x^2, sigma_x] = 0 (iii) (sigma vector . A vector)(sigma vector . B vector) = A vector . B vector + i sigma vector . (A vector x B vector) if A vector and B vector commute with Pauli matrices.

A body moving in an inverse square attractive field traverses on elliptical orbit with eccentricity e and period gamma. Find the time taken by the body to traverse the half of the orbit that is nearer the centre of force. Explain briefly why a comet spends only 18% of its time on the half of its orbit that is nearer the sun.

In Michelson interferometer, 100 fringes cross the field of view when the movable mirror is displaced through 0.029 mm. Calculate the wavelength of the light source used.

Explain the principle of (i) induced absorption, (ii) spontaneous emission and (iii) stimulated emission. Show that the ratio of Einstein's coefficients is given by A/B = 8 pi h v^3 / c^3

In the circuit diagram shown below, the voltmeter reads 50 volts when it is connected across the 400 ohm resistance. Calculate what the same voltmeter will read when connected across the 300 ohm resistance.

The equation of a progressive wave moving on a string is y = 5 sin pi(0.01x - 2t). In this equation, y and x are in centimetres and t is in seconds. Calculate amplitude, frequency and velocity of the wave. If two particles at any instant are situated 200 cm apart, what will be the phase difference between these particles?

With the help of a neat diagram, show that the potential due to a dipole at a point is given by V = (1 / 4 pi epsilon_0) * (p cos theta / r^2), where p is the dipole moment of the charge distribution, theta is the angle between the line joining the centre of the dipole to the point of interest and the axis of the dipole.

A horizontal pipe of non-uniform bore has water flowing through it such that the velocity of flow is 40 cm/s at a point where the pressure is 2 cm of mercury column. What is the pressure at a point where the velocity of flow is 60 cm/s? (Take, g = 980 cm/s^2 and density of water = 1 g/c.c.)

What is Lamb shift ? What is its significance in determining the fine structure of H_alpha Balmer line in hydrogen atom ?

Write down the salient features of the Einstein's theory of lattice heat capacity. Further write down the expression for specific heat in Einstein's theory and explain its high and low temperature limits.

Four solid spheres A, B, C and D, each of mass m and radius a, are placed with their centres on the four corners of a square of side b as shown in the figure below : Calculate the moment of inertia of the system about one side of the square. Also calculate the moment of inertia of the system about a diagonal of the square.

(i) The viscosity in a liquid arises due to friction between adjacent layers. What causes viscosity in a gas? Explain. (ii) The molecules of a gas obeying Maxwell-Boltzmann distribution move with an average speed of 450 m s^-1. If the coefficient of viscosity of the gas eta is 16.6 x 10^-6 N s m^-2, density of the gas rho is 1.25 kg m^-3 and number density is 2.7 x 10^25 m^-3, calculate the mean free path and diameter of the gas molecules.

Write down Maxwell's equations for linear dielectrics and deduce the equation of continuity.

Explain why the deuteron has no excited state.

Briefly explain Planck's law of blackbody radiation. Show that Planck's law reduces to Wien's law and Rayleigh-Jeans law at lower and higher wavelength limits respectively.

An alternating current varying sinusoidally with a frequency of 50 Hz has an r.m.s. value of 40 A. Find the instantaneous value of the current at 0.00125 second after passing through maximum positive value.

Obtain Laue's equations for X-ray diffraction by crystals. Show that these are consistent with the Bragg's law.

An electron is confined to move between two rigid walls separated by 10^-9 m. Compute the de Broglie wavelengths representing the first three allowed energy states of the electron and the corresponding energies.

Given a proton for which beta = 0.995 measured in the laboratory. What are the corresponding relativistic energy and momentum? Take, m_p = 1.67 x 10^-24 g.

Calculate the percentage contraction in the length of a rod in a frame of reference, moving with velocity 0.8c in a direction (i) parallel to its length and (ii) at an angle of 30 degrees with its length. What is the orientation of the rod in the moving frame of reference in case (ii)?

Solve the Schrodinger equation for a step potential and calculate the transmission and reflection coefficient for the case when the kinetic energy of the particle E_0 is greater than the potential energy V (i.e., E_0 > V).

The molecules of a gas obey Maxwell-Boltzmann distribution. Calculate the fraction of molecules of the gas within 1% of the most probable speed at STP. Interpret your result.

What are elementary particles and how are they classified ? Describe in brief the different types of interactions that can occur between the elementary particles.

What is the difference between direct and indirect band gap semiconductors ? Which one is suitable for use in solar cells ?

In free space, the electric field of electromagnetic wave is given as E_vector(x, t) = 120 cos(wt - kx) y_hat V/m. Find the average power crossing a circular area of radius one metre in the yz-plane.

Derive the expression for Coriolis force and show that this force is perpendicular to the velocity and to the axis of rotation. What is the nature of this force?

The spectral energy curve of the moon shows maxima at 470 nm and 14 micrometer. What inference can you draw from this data? Also calculate the energy density and radiation pressure in both cases. Given, Wien's constant b = 2.892 x 10^-3 m K, Stefan's constant sigma = 5.67 x 10^-8 J m^-2 s^-1 K^-4 and speed of light c = 3 x 10^8 m s^-1.

Calculate the density of states for an electron moving freely inside a metal with the help of quantum mechanical Schrodinger's equation for free particle in a box.

m gram of water at temperature T_1 is isobarically and adiabatically mixed with an equal mass of water at temperature T_2. Show that the change in entropy is given by delta S = 2 m C_p ln(T_av / T_geo), where T_av = (T_1 + T_2)/2 and T_geo = sqrt(T_1 T_2).

The series limit wavelength of Balmer series in hydrogen spectrum is experimentally found to be 3646 angstrom. Find the wavelength of the first line of this series.

In the Stern-Gerlach experiment using Ag atoms, the oven temperature is 1000 K, l = 25 cm and dBz/dz approx 10^+3 Tesla/m. Calculate the separation of the two components.

Explain unification of electromagnetic and weak interactions. What is Z^0-boson ? What is its relevance in electroweak unification ?

Show that the Young's modulus Y, modulus of rigidity n and Poisson's ratio sigma are related by the equation Y = 2n(1 + sigma).

Find the energy, momentum and wavelength of a photon emitted by a hydrogen atom making a direct transition from an excited state with n = 10 to the ground state. Also find the recoil speed of the hydrogen atom in this process.

Show that in the nuclear shell model, the level spacing between major oscillator shells is approximately h_bar omega = 41 A^-1/3 MeV.

Explain the principle of producing polarized light by the method of reflection, refraction and double refraction with the help of neat diagrams.

With the help of a schematic diagram, show how entropy and specific heat vary with temperature for a superconductor.