UPSC Physics Optional PYQs (CSE & IFoS)PYQs

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.

A body of mass m at rest splits into two masses m_1 and m_2 by an explosion. After the split the bodies move with a total kinetic energy T in opposite direction. Show that their relative speed is \sqrt{\frac{2Tm}{m_1m_2}}.

A homogeneous right triangular pyramid with the base side a and height \frac{3a}{2} is shown below. Obtain the moment of inertia tensor of the pyramid:

A capillary tube having 1.0\,\mathrm{mm} diameter, 20\,\mathrm{cm} in length is fitted horizontally to a vessel in which alcohol is kept fully up to the neck. Density of alcohol is 8 \times 10^{2}\,\mathrm{kg/m^3}. The depth of the centre of the capillary tube below the surface of alcohol is 40\,\mathrm{cm}. Find the amount of alcohol that will flow out of the capillary tube in 10 minutes. Coefficient of viscosity of alcohol is 0.0012\,\mathrm{N\,s/m^2}.

The radius of the Earth is 6.4 \times 10^{6}\ \mathrm{m}, its mean density is 5.5 \times 10^{3}\ \mathrm{kg/m^{3}} and the universal gravitational constant is 6.66 \times 10^{-1}\ \mathrm{Nm^{2}/kg^{2}}. Calculate the gravitational potential on the surface of the Earth.

Consider an amplifier with an open-loop (no feedback) gain of A and a feedback factor \beta. Derive the expression for the gain with feedback, A_f. Derive the condition for the amplifier with feedback to act as an oscillator. Comment on the change in A_f with a change in A.

The lattice parameter and the atomic mass of a diamond crystal are 3.57\,\mathring{\mathrm{A}} and 12, respectively. Calculate the density of the crystal. Given, Avogadro's number, N = 6.023 \times 10^{26}\,(\mathrm{kg\ mol})^{-1}.

In an almost pure thick aluminium sheet, there are 0.19 atomic percent of copper at the surface and 0.18 atomic percent at a depth of 1.2\,\mathrm{mm} from the surface. Calculate the flux of the copper atoms from the surface at 550^\circ\mathrm{C}, if the diffusion coefficient of copper in aluminium at this temperature is 5.25 \times 10^{-13}\,\mathrm{m^2\,s^{-1}}. Given, Al FCC with lattice parameter, a = 4.05\,\mathring{\mathrm{A}}.

What is an intrinsic semiconductor? Intrinsic silicon has a band gap of 1.1\,\mathrm{eV} and yet at T=300\,\mathrm{K}, the conductivity is non-zero. Explain. Comment, with the help of relevant expression, on the position of the Fermi level of an intrinsic semiconductor.

List in two separate columns, the quantities that are conserved and not conserved in the weak interaction of particles.

Write down the Weizsäcker mass formula for the nuclear binding energy. Give short justification for each term of the formula.

Write down the basic weak interaction processes in the nuclei. Also illustrate the beta decays of (i) neutron and (ii) proton.

Natural uranium found in the earth's crust contains the isotopes {}^{235}_{92}\mathrm{U} and {}^{238}_{92}\mathrm{U} in the atomic ratio 7\cdot3\times10^{-3} to 1. Assuming that at the time of formation these two isotopes were produced equally, estimate the time since formation. Given that the mean lives of both the isotopes are 1.03\times10^{9} years and 6.49\times10^{9} years, respectively.

Explain the Mössbauer effect.

List the main reactions in the pp chain leading from hydrogen to helium during stellar nucleosynthesis. Also mention the net effect of the reactions.

Calculate in terms of the nuclear magneton, \mu_{\mathrm{N}}, the magnetic dipole moment of {}^{3}S_{1} state of deuteron. Given, \mu_{\mathrm{p}}=2\cdot792847\mu_{\mathrm{N}} and \mu_{\mathrm{n}}=-1.913042\mu_{\mathrm{N}}.

Explain how the magnetic moments of atoms, the space quantization of angular momentum and the spin of electron are measured using Stern–Gerlach experiment.

Calculate the frequency of the first Bohr orbit of hydrogen atom.

Write the principle of nuclear magnetic resonance (NMR). Explain the design and working of NMR, and write its important applications.

Determine the normal Zeeman splitting of the cadmium red line of 6438\,\mathring{\mathrm{A}}, when the atoms are places in a magnetic field of 0.009\,\mathrm{T}.