UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Calculate the temperature at which the average speed of \text{H}_2 molecules equals that of \text{O}_2 molecules at 350\text{ K}.

A shower of 6 \times 10^3 molecules, each travelling initially with same velocity, traverses a gas. Estimate the number of molecules which will travel unaffected even after traversing a distance equal to twice the mean-free path.

Define the thermodynamic energy functions. Using these functions establish the following relations:

(i) \left(\frac{\partial T}{\partial V}\right)_{\phi} = -\left(\frac{\partial P}{\partial V}\right)_V

(ii) \left(\frac{\partial P}{\partial T}\right)_V = \left(\frac{\partial \phi}{\partial V}\right)_T

(iii) \left(\frac{\partial T}{\partial P}\right)_{\phi} = \left(\frac{\partial V}{\partial \phi}\right)_P

(iv) \left(\frac{\partial \phi}{\partial P}\right)_T = -\left(\frac{\partial V}{\partial T}\right)_V

Write a short note on Equipartition of energy.

Write a short note on Joule-Kelvin effect.

Show that the temperature (T) of a plant varies inversely as the square root of its distance (R) from the Sun. (The Sun and Planets are considered to be black-bodies in radiative equilibrium.)

State Biot-Savart's law. Derive an expression for the magnetic field at points along the axis of a circular coil.

Write down Maxwell's equations for an isotropic homogenous dielectric and point out their relations with observational laws. How do the equations lead to the concept of electromagnetic waves?

Write a short note on Uniqueness theorem in electrostatics.

State Coulomb's law and show that the electric field can be derived from a potential function. If the charge distribution is continuous, find the integral formula for determining its field.

The total energy, U in oscillating L-C circuit is given by: U = U_B + U_E = \frac{1}{2} L i^2 + \frac{1}{2} \frac{q^2}{C} When the resistance of the circuit is zero From this show that it is an oscillatory circuit and find the time period.

State Planck's formula for black-body spectrum. Show that 'Planck's formula reduceds to Wien's formula at short wavelengths,

If steady voltage is applied to an L-R circuit, show how voltage across the inductance and the current in the circuit changes with time. Explain the term inductive time constant.

In a nuclear explosion, the maximum temperature reached was of the order of 10^8\text{ K}. Estimate the order of wavelength at which the maximum of radiated energy occurs.

A particle executing simple harmonic motion, has an acceleration (\pi^2/3)\text{ cm/sec}^2 when the displacement is 1\text{ cm}. Determine the period.

A ruby laser produces a beam of light of wavelength 0.3\text{ \AA} with a circular cross-section 1\text{ cm} in diameter. Calculate the diameter of this beam at a distance of 1000\text{ kilometers}.

Give an outline of Fresnel's explanation of optical rotation. How does optical rotation due to a material vary with \lambda? For an optically active material the difference between the refractive indices for right-handed and left-handed vibrations (\mu_R - \mu_L) for \lambda = 4500\text{ \AA} is 12 \times 10^{-5}. Estimate the optical rotation caused by 1\text{mm} thick plate in light of 1 = 4500\text{ \AA}. [Assume (m_R - m_L) as independent of \mu.]

State Rayleigh Criterison for limit of resolution. Show that \frac{I_{\text{middle}}}{I_{\text{max}}} = \frac{8}{\pi^2}

Show that the particle velocity in case of a plane progressive wave is given by \frac{\partial y}{\partial t} = -V \frac{\partial y}{\partial x} (where V is the wave velocity). Hence obtain the differential equation of wave motion.

Distinguish between Fresnel and Fraunhofer classes of diffraction of light. Discuss the theory of a plane grating and hence find an expression for the angular dispersion of a plane grating.