Deduce the magnitude and direction of the acceleration of the moon and new moon.

An electron with velocity 4 \times 10^6\text{ m/s} approaches a point nucleus from a great distance with an impact parameter 0.5 \times 10^{-10}\text{ m}. Calculate the angular momentum of the electron about the nucleus. Show that the electron scattering is S-wave scattering.

A sphere of radius a_1 made of a material of density p_1 falls through a fluid with terminal velocity v_1. Another sphere of radius a_2 made of a material of density p_2 falls through the same liquid with terminal velocity v_2. Assuming that the viscous dreg for these particles is given by \pi \eta a v. show that the viscosity of the fluid is given by \frac{2 g a_1^2 a_2^2 (p_2 - p_1)}{9 (a_1^2 v_2 - a_2^2 v_1)}

Write a note on Coriolis force.

Write a note on Addition theorem of velocities in special theory of relativity.

Define differential scattering cross-section for a scattering process, the differential scattering cross-section for neutrons scattered elastically from a solid is of the form \alpha(\theta) = A c^{-B(\vec{K}_i \cdot \vec{K}_f)^2} where A and B are constants and \vec{K}_i and \vec{K}_f are respectively the wave vectors of the incident and scattered neutron. Determine the total scattering cross-section. [\vec{K}_i] = [\vec{K}_f]

Prove that if E and E' are respectively the neutron energies in the laboratory system, before and after collision with a nucleus of mass number A. then \frac{E'}{E} = \frac{1 + A^2 + 2 A \mu_e}{(1 + A)^2} where \mu_e is the cosine of the scattering angle in the centre of mass system.

A body falls from a great height towards the surface of the moon. Write down its equation of motion and solve it to determine the speed with which the body strikes the surface. Also find its numerical value.

How is a p-n junction prepared? Explain the charge and potential distributions in such a junction in open circuit. Explain how a p-n junction can be used to build a solar cell. Describe the mechanism of the increase of conductivity of Germanium by doping it with Arsenic.

What is superconductivity? In what kind of materials is it found to occur? Name some parameters which characterise a superconductor. Cite any two major use if we succeed in making superconductors with T_c not far atmospheric temperatures.

Write a brief scientific note on Transistor as an amplifier.

Write a brief scientific note on Logic gates and their applications.

Two isotopes of oxygen have nuclear masses 15.990523 a.m.u. and 17.994768 a.m.u. Calculate the binding energy per nucleon in the two cases in MeV. What do you expect about the relative abundances of the two isotopes?

Write a brief scientific note on Linear particle accelerators.

Give an example of nuclear fusion and explain how energy is released in the process. In nature fusion reactions are often brought about by height temperatures. Explain the role of high temperature and the relevance of quantum effect in this.

Write a brief scientific note on Elementary particles and their classification.

Radium has a half-life of 1600 years and the daughter nucleus Radon also decays with a half-life of 3.82 days. In an enclosure containing radium and radon gas, the amount of radon appears to be constant for observations extending over a week. Explain this and calculate the ratio of the numbers of radium nuclei. Will the amount of radon remain the same even after 400 years?

State the laws followed in \alpha-decay by different radioactive nuclei and outline the theory which explained \alpha-decay

What are the transitions leading to the emission of the D lines of Sodium? Deduce the expression for the Lande splitting factor. g and calculate its values for the states involved in the emission of D lines. Hence find the change of energies of these levels when a sodium source is placed in a magnetic field which is not too high.

Discuss how stars are classified on the basis of their spectra. Briefly mention what different informations about stars can be obtained from the study of their spectra.