The refractive indices of material of wavelength 5090\text{ \AA}, 5340\text{ \AA} and 5890\text{ \AA} are equal to 1.64, 1.640 and 1.630 respectively. Estimate the phase group velocities of light near \lambda = 5340\text{ \AA}.

N coherent oscillation given by \zeta_K a \cos = (\omega t + K \phi) \quad K = 1, 2, 3, \ldots N are added, where a and \phi are independent of K. Deduce the expression for amplitude of the resultant oscillation.

A rocket of mass 1000\text{ kg} is ready for a vertical take off. The exhaust velocity of its fuel is 4.5\text{ km/s}. Deduce (i) the minimum rate of fuel ejection so that the rocket weight be just balance, (ii) the velocity acquired in 8\text{ s} if the fuel ejection rate is 2.50\text{ kg/s}. (You may neglect the effect of changing mass of the rocket in the given conditions.)

Find the fractional decrease of kinetic energy of a particle of mass m_1 when a head-on elastic collision takes place with another particle of mass m_2 initially at rest. In this context show why hydrogen would be best to be used for slowing down neutrons. Actually \text{D}_2\text{O}, not \text{H}_2\text{O} is used why?

Prove that the rate of angular momentum of a system about a fixed line is equal to the total torque of the external forces about that line

A top is spinning with an angular velocity \omega about its axis which is initially vertical Find the condition of stability, if the axis be given a slight nutation.

Write a short note on Conchs forces.

Define Reynold's number, the cross sectional radius of a pipeline decreases following the relation. r = r_0 e^{-ax}, where a = 0.6\text{ m}^{-1}, x is the distance (in \text{m}) from the pipeline inlet. Calculate the ratio of Reynold's number for two cross sections separated by \Delta x = 3\text{m}.

A radioactive nucleus mass m_0\text{ amu} emits an alpha particle with kinetic energy E_a. If the disintegration occurs when the nucleus is free, deduce an expression for the energy evolved (E_t) during the disintegration.

State Lorentz transformation equations. Show that for v/c \ll 1, the lorentz transformation equations reduce to Galilean transformation equations. Explain the physical significances of Larentz transformations.

Write a short note on Mass energy equivalence.

A satellite, revolving in a circular equatorial orbit at height 1.36 \times 10^4\text{ km} from earth's surface from west to east, appears over some spot at the equator every 6\text{ hrs}. Show that the data are consistent with known earth's radius 6.4 \times 10^3\text{ km} and g = 9.8\text{ ms}^{-2} at earth's surface.

Write a short note on Rutherford Scattering.

Write a short note on superconductivity.

Write a short note on zener diode.

What will happen to output voltage of an amplifier if a part of the output is returned to the input (i) in phase (ii) 180^\circ out of phase ?

If a signal from a high impedance source is to be amplified, which configuration is preferred and why?

Explain the formation of potential barrier in an unbiased p-n junction.

What is the role of transistor in an amplifier?

Write a short note on Para and ferromagnetism.