UPSC Physics Optional PYQs (CSE & IFoS)PYQs

A particle is moving under a central force field. Obtain the equations of motion and prove that in such a field the areal velocity of the particle remains constant.

Obtain the relativistic transformation relation for density in inertial frames. Why is the equivalent energy corresponding to 1 amu of mass?

Distinguish between streamline and turbulent motion. Define Reynolds number. When a sphere of radius 1.2\text{ mm} moves in glycerine, the laminar flow observed if the velocity of sphere does not exceed 0.23\text{ ms}^{-1}. At that minimum velocity of sphere of radius 5.5\text{ cm} will the flow in water become turbulent? The viscosities of glycerine and water are 11.9\text{ P} and 0.011\text{ P} respectively. The density of glycerine is 1.2 \times 10^{-3}\text{ Kg/m}^3.

Explain processional motion of a top. A solid sphere of radius 2\text{ cm} and mass 50\text{ gm} has a thin nail of length 5\text{ mm} fixed perpendicular to its surface. When this sphere spins like a top with a speed of 20 rev./second what will be its processional speed?

Moving in a closed elliptical orbit, Halley's comet goes round the Sun once every 75 years. At its point of closest approach its distance from the Sun is 8.9 \times 10^7\text{ km}. If mass of the Sun is 2 \times 10^{30}\text{ kg}, what will be the greatest distance of the comet from the Sun ?

A Si BJT is connected as shown Fig . Show that it is in active region and works as an amplifier Calculate its mid frequency gain, given that BJT has h_{ie} = 1\text{ k}\Omega, h_{oe} = h_{re} = 0, I_{co} = 20\text{ nA}.

Define ex-OR. Give its truth table and draw the possible logic blocks.

Derive the expression for the frequency spectrum of a carrier wave of frequency f_c which is amplitude modulated by a frequency f_m. A certain transmitted radiates 9\text{ kW} of power when the carrier wave is unmodulated and 10.12\text{ kW} power when the carrier wave is sinusoidally modulated. Calculate the modulation index.

Taking only the spin motion of electron, proton and neutron and assuming them as point particles, obtain their magnetic moments. How far the values thus obtained agree with experimental values? If not, why? Explain.

Write a comparative account of the following four processes: (i) \beta - decay (ii) positron emission (iii) electron capture (iv) inverse \beta- decay

Define parity for a quantum mechanical system. Describe an appropriate experiment proving the parity violation in weak interaction. How can the parity violation in weak interaction be understood ? Explain.

Calculate the bond length and force constant of the bond of {}^{12}\text{C}\ {}^{16}\text{O} molecule; given 0 \rightarrow 1 rotational line in v = 0 state is at 115.3\text{ GHz} and the wavelength of the vibrational frequency is 14.7\ \mu\text{m}.

Explain the fine structure of H_\alpha line of H-atom arising due to LS coupling.

Write a short note on Stellar spectra.

Describe Frank Hertz experiment to establish the quantization of energy levels.

Calculate the velocity and direction of recoil electron for back scattered X-ray photon of \text{Mo } K_\alpha of 0.707\ \text{\AA} in Compton effect.

An electron moving with energy E encounters one dimensional potential step as given below: V(x) = 0 \quad x < 0 \qquad V(x) = V_0 \quad x > 0 (a) Suppose the electron has the energy E > V_0 and is incident from (-x) direction, find the normalized wave function so corresponds to unit incident flux. (b) Solve the above problem for the case E < V_0 and discuss the significance of the result with the help of a suitable example.

Explain the concept of entropy The specific heat C_p of a material depends on temperature T according to the relation: C_p = a + bT + cT^2 \text{ where a, b and c are constants,} Derive an expression for the change in its entropy when the temperature changes from T_1 to T_2.

How is absolute scale of temperature obtained with the help of Carnol cycle? Hence define absolute zero

To what extent the pressure in a cathode ray tube must be reduced so that 90\% of the electrons emitted by the cathode reach the anode which is at a distance of 20\text{ cm} from the cathode? The mean molecular radius of main constituent gases of atmosphere is 2\text{\AA} and the number of molecules at standard pressure (760\text{ mm of Hg}) is 3 \times 10^{25} per \text{m}^3.