UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Obtain the equation of motion of a particle moving relative to a rotating frame of reference. Explain the term representing coriolis force in this expression.

A system with 2 independent coordinates x_1 and x_2 has the following Larangian L = \frac{1}{2} \frac{(\dot{x}_1)^2}{\alpha + \beta x_2} + \frac{1}{2} (\dot{x}_2)^2 (x_2)^2 - \gamma x_2 \alpha, \beta, \gamma being constants. Obtain the Lagrangian equation of motion.

Define scattering cross-section. A charged particle of mass m and charge Z_e is scattered by another charged particle of charge Z_e at rest. Deduce the expression for the scattering cross-section.

A person in a spaceship is holding a rod of length of 0.5 m, the space ship is cruising at a speed V parallel to the earths surface. What does the person in the space ship notice as the rod is rotated from parallel to perpendicular to the space ships motion? What does an observer on earth's surface notice?

Determine equation of trajectory for a particle under central force `F', the magnitude of which is given by F = -\frac{A}{r^2} + \frac{B}{r^3} where A and B are positive constants.

The mass of muon at rest is 207\text{ m}_e where m_e is the electron rest mass (0.511\text{ MeV}). The mean life time at rest for muon is 2.2\ \mu\text{s}. The life time of muon emerging from an accelerator is measured in the laboratory as 6.9\ \mu\text{s}. Estimate the speed of these muons in the laboratory.

A star of the size of our sun having a radius of 7 \times 10^5\text{ km} and having a mass 2 times as that of the sun is rotating at a speed of one revolution every 10 days. If the star undergoes a gravitational collapse to a neutron star of radius 10\text{ kms}, assuming that the star is a uniform sphere at all times, calculate the rotation speed of the neutron star. The moment of inertia of solid about its diameter is 2/5\text{ MR}^2 where M and R are the mass and radius of the solid sphere respectively.

Which one of these mechanisms shows a negative dynamic resistance? Why?

A circuit of a NOT gate is given in the figure below. Explain how you will determine the values of the resistances R_B, R and R_L.

Discuss the different breakdown mechanisms for a reverse biased Zener diode.

A Zener diode of 1\text{ W} power has a dynamic resistance of 10\text{ m}\Omega at the breakdown voltage of 3\text{ V}. What will be the fluctuations in the current through the diode if the voltage fluctuates by 100\text{ mV}? What will happen to the diode ? Why?

Do these mechanisms have different temperature coefficients? Explain.

Explain why superconductors are perfect diamagnets.

What are the salient characteristics of ferromagnetic ? Explain how the Curie law of paramagnetism is modified to the Curie - Weiss law.

A nuclear reactor has an output power of 1\text{ MW} with a thermal efficiency of 30\%. How much uranium per day is consumed to run this reactor, if the average energy released per fission of {}^{235}\text{U} is 200\text{ MeV}, and the uranium is enriched to 2\%\ {}^{235}\text{U} ?

Which of the following reactions are allowed? What are the conservation laws violated by the rest ? Classify the particles (fermions / bosons. mesons / baryons, leptons/ hadrons) involved and the type of interactions in the case of the allowed ones. (i) \Sigma^0 \rightarrow \pi^+ + \pi^- (ii) \pi^- + p \rightarrow n + \pi^0 (iii) \pi^+ + p \rightarrow \pi^+ + p + \pi^- + \pi^0 (iv) \pi^0 \rightarrow \gamma + \gamma

How do you explain the continuous spectrum in beta decay of radioactive nuclei ?

Using the uncertainty principle, show that the electrons cannot exist inside the nucleus. How does then one account for the beta decay of a nucleus ?

A \mu (of mass 207\text{ m}) is in the ground state of a muonic atom whose nucleus is Pb (Z = 82, A = 204, and radius = 7\text{ fm}). Calculate the first Bohr radius in units of the nuclear radius and the Rydberg constant in units of the Rydberg constant in units of the Rydberg constant of the hydrogen atom. Comment on your results.

Determine all the Term symbols of p^2 equivalent electrons and arrange these states in increasing order of energy. Justify your answer.