UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Show that two light beams polarized in perpendicular directions will not interfere.

In the propagation of longitudinal waves in a fluid contained in an infinitely long tube of cross-section A, show that \rho=\rho_0\left(1-\frac{\partial\xi}{\partial x}\right) where, \rho_0 = equilibrium density \rho = density of the fluid in the disturbed state \frac{\partial\xi}{\partial x}=\text{volume strain}\quad\left(\left|\frac{\partial\xi}{\partial x}\right|\ll1\right)

Obtain the expression for the primary focal length of Fresnel zone plate.

When a sphere of radius r falls down a homogeneous viscous fluid of unlimited extent with the terminal velocity v, the retarding viscous force acting on the sphere depends on the coefficient of viscosity \eta, the radius r and its velocity v. Show how Stokes' law was arrived at connecting these quantities from the dimensional considerations.

What is the significance of the null result of Michelson-Morley experiment? Does it disprove the existence of ether? Justify.

A planet revolves around the Sun in an elliptic orbit of eccentricity e. If T is the time period of the planet, find the time spent by the planet between the ends of the minor axis close to the Sun.

A uniform solid sphere of radius R having moment of inertia I about its diameter is melted to form a uniform disc of thickness t and radius r. The moment of inertia of the disc about an axis passing through its edge and perpendicular to the plane is also equal to I. Show that the radius r of the disc is given by r=\dfrac{2R}{\sqrt{15}}.

What are Eulerian angles? A body with rotational symmetry about an axis is rotating under gravity about a point on the axis without friction. What are the quantities remaining constant during the motion? Find them in terms of suitable Eulerian angles. Explain 'precession' and 'nutation' of such a body.

Which of the waves out of (i) X-rays, (ii) de-Broglie waves due to electrons or neutrons will be suitable for crystal diffraction ? Justify your answer in terms of energies of these waves for 0 \cdot 1 \text{ nm}.

A type-II superconducting material with superconducting transition temperature T_c is placed in a magnetic field. What is the material state (normal or superconducting or mixed) for (i) T < T_c ; \quad H > H_{c_2} (ii) T > T_c ; \quad H < H_{c_1} (iii) T < T_c ; \quad H_{c_1} < H < H_{c_2} (iv) T < T_c ; \quad H < H_{c_1} (v) T > T_c ; \quad H > H_{c_2} where H_{c_1} and H_{c_2} are the lower and upper critical fields for a type-II superconductor.

Show that the reciprocal lattice of a hexagonal lattice is a hexagonal lattice with a rotation of axes.

Silicon is the most popular semiconductor material used for the fabrication of electronic devices and integrated circuits. Why ? Give at least five reasons.

The resistance of silicon and germanium varies with temperature. But these are not used normally as thermistors. Why ? Name at least two widely used materials for making thermistors and give any five applications of thermistor.

List the characteristics of an ideal OP-AMP. Write the expression for the output voltage in terms of input voltages and resistance values.

What do you understand by early effect in bipolar junction transistors ? What are its consequences ? Discuss briefly the advantage of using the BJT in the common collector configuration.

What is Meissner effect ? Explain the conclusions drawn from the Meissner effect.

Verify that the circuit shown below is an exclusive OR.

Compare the methods of electron scattering and neutron scattering experiments to obtain information about nuclear size.

What are the field quanta of weak and electromagnetic interactions ? Show that weak interaction is a short range force while electromagnetic interaction is a long range one.

At what energies, do we anticipate the unification of strong and electroweak interactions ? What will happen to coupling constants of these interactions in this situation ? How does unification indicate the decay of proton and existence of leptoquark ?