Why does a soap bubble expand upon electrification? A sphere of radius R contains a charge +Q and a charge -Q distributed uniformly in the upper and lower hemispheres respectively. Show that the dipole moment of charge distribution is \dfrac{3}{4}QR\hat{k}, where \hat{k} is directed along the polar axis of the spherical coordinate system.
Discuss the principle of 'artificial dielectric'. Where do you find its use?
A charge q=2\,\mu\mathrm{C} is placed at a=10\,\mathrm{cm} from an infinite grounded conducting plane sheet. Find the (i) total charge induced on the sheet, (ii) force on the charge q and (iii) total work required to remove the charge slowly to an infinite distance from the plane.
Obtain the system matrix for a thin lens placed in air and made of material of refractive index 1.5 having radius of curvature 50\,\mathrm{cm} each. Also find its focal length.
Find the velocity of sound in a gas in which two waves of wavelengths 1.00\,\mathrm{m} and 1.01\,\mathrm{m} produce 10 beats in 3 seconds.
Explain with proper example the interferences due to 'division of wavefront' and 'division of amplitude'.
A plane-polarized light passes through a double-refracting crystal of thickness 40\,\mu\mathrm{m} and emerges out as circularly polarized. If the birefringence of the crystal is 0.00004, then find the wavelength of the incident light.
What is multiple-beam interference? Discuss the advantages of multiple-beam interferometry over two-beam interferometry. Explain the fringes formed by Fabry-Perot interferometer.
Show that the areas of all the half-period zones are nearly the same. Find the radius of 1st half-period zone in a zone plate whose focal length is 50\ \mathrm{cm} and the wavelength of the incident light is 500\ \mathrm{nm}.
How is laser light different from ordinary light? Discuss the working principle of ruby laser. What role do chromium ions play in this process?
Explain the principle of operation of optical fibre. What are the different losses that take place in optical fibre?
Sunlight is reflected from a calm lake. The reflected light is 100% polarized at a certain instant. What is the angle between the sun and horizon?
Prove that x^2+y^2+z^2=c^2t^2 is invariant under Lorentz transformation.
Describe Michelson-Morley experiment and show how the negative results obtained from this experiment were interpreted.
Define moment of inertia and explain its physical significance. Calculate the moment of inertia of an annular ring about an axis passing through its centre and perpendicular to its plane.
State and explain Stokes' law. A drop of water of radius 0.01\ \mathrm{m} is falling through a medium whose density is 1.21\ \mathrm{kg/m^3} and \eta = 1.8 \times 10^{-5}\ \mathrm{N\,s/m^2}. Find the terminal velocity of the drop of water.
Express angular momentum in terms of kinetic, potential and total energy of a satellite of mass m in a circular orbit of radius r.
A diatomic molecule can be considered to be made up of two masses m_1 and m_2 separated by a fixed distance r. Derive a formula for the distance of centre of mass, C, from mass m_1. Also show that the moment of inertia about an axis through C and perpendicular to r is \mu r^2, where \mu=\dfrac{m_1m_2}{m_1+m_2}.
A ball moving with a speed of 9\ \mathrm{m/s} strikes an identical stationary ball such that after the collision the direction of each ball makes an angle 30^\circ with the original line of motion. Find the speed of the balls after the collision. Is the kinetic energy conserved in this collision?
What is the difference between direct and indirect band gap semiconductors? Which one is suitable for use in solar cells?
