UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Neptune's period of revolution is 165\text{ yr}. What is the average radius of Neptune's orbit in teams of the Sun-Earth distance?

Derive an expression for the mass-energy equivalence using the principle of special relativity.

An aeroplane makes a complete half circle of 50\text{ m} radius towards left when flying at 200\text{ km / hour}. The rotary engine and the propeller of the plane weigh 400\text{ kg} having a radius of gyration of 30\text{ cm}. The engine rotates at 2400\text{ rpm} clockwise viewing from the rear. Find the gyroscopic couple on the aircraft.

How is frequency modulation advantageous compared to amplitude modulation? Still, why are the video signals transmitted by television stations amplitude modulated?

What is Meissner effect? Superconducting tin has a critical temperature of 3.7 K in zero magnetic field and critical field at 0 K is 306 gauss. Determine the critical field at 2K.

Simplify the given Boolean expression and draw the corresponding logic circuit using NAND gates: Y = (\bar{A} + B + C) . (\bar{A} + \bar{B} + C)

A junction diode in series with a parallel combination of a large resistor and a capacitor acts as a linear detector of amplitude modulated waves. Explain the action.

Phosphorous is doped in a silicon wafer. The impurity concentration is 10^{13}\text{ per cm}^3. If all the donors are active calculate its resistivity at room temperature. The mobility of electrons is 1250\text{ cm}^2/\text{V-s}.

The specific activity of a sample containing radioactive \text{Co}^{58} and non-radioactive \text{Co}^{59} was observed to be 2.2 \times 10^{12} disintegrations per second per gm. Half-life of \text{Co}^{58} is 71.3 days. Find the percentage of mass of radioactive element in the sample.

Give Weiszacker formula for the binding energy of a nucleus. Explain the significance of each term. Derive an expression for the atomic number Z of the most stable nucleus for a given mass number A. Determine the atomic number Z of the stable nucleus having A = 64.

The following reaction do not take place : (i) n \rightarrow p + e^- + \nu (ii) p \rightarrow \pi^0 + e^+ + \nu Explain the reasons in terms of conservation laws.

For a particle confined in a one dimensional potential well of length L the wave-function is \psi(x) = c \sin (\pi x/L), 0 < x < L and \psi(x) = 0. \text{ outside} Calculate the expectation values of x and p.

What are Compton effect and Compton wavelength ? Determine Compton shift. Show that maximum Compton shift is twice the Compton wavelength.

Using the uncertainty principle \Delta x . \Delta p \sim h/2, estimate the minimum energy of a particle in a simple harmonic potential U = 1/2 k x^2.

Find the de Broglie wavelength associated with an electron of energy (i) 10 eV and (ii) 10 MeV

What is spin-orbit coupling? Considering the sodium doublet (5890\text{ \AA} and 5896\text{ \AA}), calculate the effective magnetic field experienced by the electron in the 3p state.

Explain how very low temperatures can be produced by adiabatic demagnetisation.

The RMS speed of oxygen molecules at 0^\circ\text{ C} is 460\text{ ms}^{-1}. What would be the RMS speed of Argon molecules (Mol. wt. = 40 gm/mole) at 40^\circ\text{ C} and at what temperature this speed would be double than at N.T.P.?

At the N.T.P., the mass of one litre of Hydrogen is 0.09 gm. Calculate the (i) RMS (ii) Mean and (iii) Most Probable Speed at 27^\circ\text{ C}.

Mention the assumptions made & by Einstein in explaining the variation of specific heat of solids with temperature. Show how these assumptions were used to derive the formula for the specific heat of solids. How and why Einstein's theory fails at very low temperatures.