UPSC Physics Optional PYQs (CSE & IFoS)PYQs

A meson of rest mass \pi comes to rest and disintegrates to a muon of rest mass \mu and a neutrino of zero rest mass. Show that the kinetic energy of motion of the muon is T = \frac{(\pi - \mu)^2 c^2}{2 \pi}

What do you mean by the moments and products of inertia ? Show that the angular momentum vector is related to the angular velocity components by linear transformation relations.

For a freely falling body from the height h' on the surface of the earth in the northern hemisphere with a latitude \theta, show that the deviation of the body towards east at the final stage is given by \frac{1}{3} \omega \cos \theta \left(\frac{8h^3}{g}\right)^{1/2}, where \omega is the angular velocity of the earth and 'g' is the acceleration due to gravity.

If a single stage rocket is fired vertically from rest at the earth's surface burns its fuel in a time of 30 sec and their relative velocity = 3 km sec{}^{-1}, what must be the mass ratio m_0/m for a final velocity v of 8 km sec{}^{-1} ?

(i) What are high T_c superconductors ? Give two examples indicating their transition temperatures. Differentiate between the conventional and high T_c super conductors. (ii) Explain the principle of feedback in an amplifier. What are the advantages & negate feedback?

In the following circuit, Show that the stability factor, S, is given by

S = \frac{1 + \beta}{1 + \frac{\beta R_e}{R_e + R_b}} Where R_b = \frac{R_1 R_2}{R_1 + R_2}

What is a Josephson junction ? Discuss dc and ac Josephson effects and obtain the relation. V = \frac{2eV}{h} where the symbols have their usual meaning.

Derive the various current components in a p-n-p transistor when it is actively biased. Using Ebers-Moll model, show that for the common-emitter configuration I_C = -\alpha I_E - I_{CO} \left(E^{V_C/V_T} - 1\right) where the symbols have the usual meaning.

Explain the operation of the following circuit is a gate. Draw the truth table and find the operation carried out by this gate neglecting the source impedance.

junction saturation voltages and diode voltages in forward direction. Find the minimum value of h_{fe}.

Calculate the gain of the following amplifier circuit :

Given that g_m = 10\text{ mV/A}, r_d = 1\ \Omega and Z_L = 10\text{ k}\Omega.

Distinguish between a nuclear reaction and decay. Which conservation laws are obeyed in nuclear reactions ? Explain the significance of Q value. Calculate the Q value for the following nuclear reaction: {}^2_1 H + ^2_1 H \rightarrow ^3_2 H + n.

Give two characteristics properties of strange par- tides which distinguish them from non-strange ones. Write the Gellmann-Nishijima relation and show how it is used for the classification of elementary particles.

Sketch carefully the binding energy per nucleon curve for stable nuclei. Explain its salient features. On the basis of this curve explain why fusion is possible only for low mass nuclei, whereas fission takes place in heavy nuclei.

List some of the important properties of deuteron and show that it is a loosely bound system and has only one bounded state.

(i) State the conservation law which is violated in each of the following processes: (1) n \rightarrow p + e^- + r (2) \pi^- + p \rightarrow K^+ + K^- (3) \pi^- + p \rightarrow \Sigma^+ + K^- (4) \Sigma^- \rightarrow K^- + p + \bar{p} (ii) Draw a bcc lattice. Determine its primitive lattice vectors and calculate the packing fraction.

Define the gyromagnetic ratio and obtain an expression for the Lande g factor. What is the importance of g factor in spectroscopy?

Discuss the salient features of O, P, Q, R and S branches of electronic spectrum of diatomic molecules. Which spectrum contains only branches, both branches and bands, branches and progressions ?

(i) What are the typical energies (eV) of the radiations, required to excite (i) electronic transitions. (ii) vibrational transitions and (iii) rotational transitions in a molecule ? (ii) The rotational spectrum of HI consists of equidistant lines with a separation of 12.8\text{ cm}^{-1}. Calculate the (a) M.I. and (b) bond length of HI molecule.

(i) Show that the radial probability density of the ground state of the hydrogen atom has a maximum at r = a. The ground state wave function of the hydrogen atom is given by \psi (r) = \frac{1}{\sqrt{\pi a^{3/2}}} e^{-r/a} where a is the Bohr radius. (ii) Calculate the Larmor frequency of a spin 1/2 particle in a magnetic field B.

(i) Express the Cartesian components of the angular momentum L in operate form. Show that [L^2, L_z] = 0. What is the significance of this commutation relation ? (ii) Show that the Pauli Matrices anti-commute.