Calculate the root-mean-square speed of smoke particles of mass 5\times 10^{-14}\text{ g} in air 0^{\circ}\text{C}.

Consider the following equation of state for a gas: P = \frac{RT}{v-b} - \frac{a}{Tv^{2}} where a and b are constants and other symbols have their usual meaning. Find the values of P_{c}, T_{c} and V_{c} in terms of a and h at the critical point.

Write a note on Super fluidity, explaining why it is a quantum phenomenon.

Write a note on Brownian motion and the importance of its study.

L, C and R in series. Discuss the factors that determine sharpness of resonance in these cases.

Write down the expression for the energy distribution of a black body radiation at temperature T and deduce. Wien's displacement law. \frac{h\omega_{m}}{kT} = \text{const.} Taking the constant to be equal to 3-\epsilon, where \epsilon is small (so that \epsilon can be neglected in comparison to 1). Find the value of \epsilon.

Calculate the power radiated by a tungsten filament 10 cm long and 0.010 mm in diameter, when it is heated to 2,500 K in an evacuated bulb. Assume that the filament radiates at 30% of the rate of a black body at the same temperature.

Write a note on Physical significance of each of the four Maxwell's equation.

Two cells of emf 2 volts each and internal resistance 2 ohms rich are connected in parallel with each other and with a load resistance. Calculate the maximum power that can be dissipated in the load.

L and R in series and C in parallel to them.

Two homogeneous isotropic dielectric media have a common plane boundary and ale otherwise infinite in extent. An electromagnetic wave is incident on the boundary. Establish the laws of reflection and refraction.

The parallel plates of a capacitor have an area of 2000\text{ cm}^2 each and are 1\text{ cm} apart. They are originally at a potential difference of 3,000\text{ volts}. When a dielectric is introduced covering the whole space between the plates, the potential difference becomes 1000\text{ volts}. Calculate the capacitance of the capacitor before and after insertion of the dielectric. What is the dielectric constant of the dielectric?

Obtain an expression for the impedance of an LCR circuit for the following cases:

How can one produce (i) left-handed circular motion, and (ii) right-handed circular motion by combining two simple harmonic motions? Justify, your answers.

Define and explain the terms resolving power and magnifying power of an optical instrument. For a telescope, on that parameter do these depend? For a given resolving power, what is the optimum magnifying power?

Out of the following three functions only one can be Fourier analysed in the range -\pi \leqslant x \leqslant \pi. Choose the correct function and obtain its Fourier series expansion: (i) f(x) = x^{2} \text{ for } 0 < x < \pi (ii) f(x) = 0 \text{ for } -\pi < x < 0 = \pi \text{ for } 0 < x < \pi (iii) f(x) = 1/x^{2} \text{ for } -\pi < x < \pi

Write a note on Uses of multiple beam interferometry.

Using Huyghens' construction, discuss the propagation of O and E waves in a biaxial crystal when the optic axis is perpendicular to the plane of incidence and parallel to the boundary surface. Take the incident ray to be oblique.

Parallel light is incident normally on diffraction grating having 6,000 lines per cm. Find the angular separation between the maxima for wavelengths 5,890 \text{\AA} and 5,896 \text{\AA} in the second order.

What is stimulated emission of light? How does it differ from spontaneous emission? Name any device basal on the stimulated emission of light and explain its working.