UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Find the capacitance of two concentric spherical metal shells having radii a and b.

Two conducting planes, intersecting at right-angles to each other, are kept at a potential \phi_0. Calculate the potential at a point in space if the total charge on a plane of area \alpha be Q.

Why do we prefer to work with a critically damped ballistic galvanometer in a laboratory? What is external critical damping resistance?

Starting from the expression for the electrostatic potential \phi(\vec{r})=\frac{1}{4\pi\varepsilon_0}\int_V\frac{\rho(\vec{r}_0)}{|\vec{r}-\vec{r}_0|}\,dV_0 obtain Poisson's equation \nabla^2\phi=-\frac{\rho}{\varepsilon_0}. [Symbols have their usual meanings]

Three cells are connected in parallel with similar poles connected together with wires having negligible resistance. The emfs of the cells are 2, 1 and 4 volts respectively and the corresponding internal resistances are 4, 3 and 2 ohms. Calculate the current flowing through the 4 V cell.

Why is population inversion in general not possible in a two-level laser system? Explain it.

Discuss how population inversion is achieved in Ruby laser. What is 'laser spiking'? Why does it occur?

What are the fringes of equal thickness and fringes of equal inclination? In a Newton's ring arrangement with a source emitting two wavelengths \lambda_1=6\times10^{-7}\,\text{m} and \lambda_2=5.9\times10^{-7}\,\text{m}, it is found that the m^{\text{th}} dark ring due to one wavelength coincides with the (m+1)^{\text{th}} dark ring due to the other. Find the diameter of the m^{\text{th}} dark ring, if the radius of curvature of the lens is 90\,\text{cm}.

How can one convert a left-handed circularly polarised light into a right-handed one (and vice versa)? Calculate the thickness of a quarter-wave plate when the wavelength of light is 589\,\mathrm{nm}. Given: \mu_0 = 1.544 and \mu_E = 1.553.

In what way is holography different from conventional photography? Discuss the salient features of a hologram. What are the requirements for the formation and reading of a hologram?

What is axial chromatic aberration? A convex lens has a focal length of 15.5 \times 10^{-2}\,\mathrm{m} for red colour and 14.45 \times 10^{-2}\,\mathrm{m} for violet colour. If an object is kept at a distance of 40\,\mathrm{cm} from the lens, calculate the longitudinal chromatic aberration of the lens.

Prove that when light goes from one point to another via a plane mirror, the path followed by light is the one for which the time of flight is the least.

(i) A reference frame S' moves with respect to rest frame S with a uniform velocity v parallel to x-direction. Show from Lorentz transformation that two events simultaneous (t_1=t_2) at different positions (x_1\ne x_2) in S frame are not in general simultaneous in S' frame.

(ii) The mean life of \pi meson is 2\times10^{-8}\,\mathrm{s}. Calculate the mean life of a meson moving with a velocity of 0.8c, where c is the velocity of light.

(i) How does Reynolds number help in the study of fluid motion?

(ii) In a horizontal pipeline of uniform area of cross-section, the pressure falls by 5\ \mathrm{N\,m^{-2}} between two points separated by a distance of 1\ \mathrm{km}. Calculate the change in kinetic energy per kg of oil flowing at these points. Density of oil = 800\ \mathrm{kg\,m^{-3}}.

Two \beta-particles A and B emitted by a radioactive source R travel in opposite directions, each with a velocity of 0.9c with respect to the source. Find the velocity of B with respect to A (Here c is the velocity of light).

(i) What is central force? Give two examples of the central force.

(ii) Show that the angular momentum \vec{L} of the particle in a central force field is a constant of motion.

Show that the cross-section for elastic scattering of a point particle from an infinitely massive sphere of radius R is \dfrac{R^2}{4}. What is the inference of this result?

Where do you find the applications of gyroscope? A top of mass 0.200\ \mathrm{kg} is made up of a thin disc of radius 0.12\ \mathrm{m}. It is pierced in the centre and a pin of negligible mass is mounted normal to its plane. The pivot under the disc is 0.03\ \mathrm{m} long. The top is made to spin with its axis making an angle \theta = 20^\circ with the vertical and a precessional angular speed of 2\ \mathrm{rad/s}. Calculate the angular speed with which it spins.

Write down Euler's dynamical equations of motion (no derivation) of a rigid body about a fixed point under the action of a torque. Show that the kinetic energy of the torque-free motion is constant.

(i) Find the moments of inertia of rigid diatomic molecule about different axes of symmetry through the centre of mass.

(ii) A proton is 1837 times heavier than an electron. Find the centre of mass of hydrogen atom.