What is the significance of the null result of Michelson-Morley experiment ? In their experiment Michelson and Morley set l_1 = l_2 = 11\text{ metres}. The wavelength of light used was 5.5 \times 10^{-7}\text{ m}. The orbital velocity of the earth is taken to be 30\text{ kms/sec}. Estimate the fringe shift to be expected.
Using Euler's equations for a force free motion of a rigid body, show that the Kinetic energy remains constant throughout the motion of the rigid body.
What are cyclic coordinates for a system of particles ? Discuss the significance of the Hamilton's principle. Show how Lagrange's equations can be derived from Hamilton's principle.
A force field is given by \vec{F} = (2xy + z^3)\hat{i} + x^2\hat{j} + 3xz^2\hat{k} Is it a conservative field ? If so, what is the scalar potential ?
Write the components of the velocity 4-vector of a particle in an inertial frame S. How does the four velocity transform to another inertial frame S' ? Obtain the Einstein's law of addition of velocities from the above transformations.
With a suitable circuit diagram and theory explain the use of OP-Amps as
(i) Adder, and
(ii) Integrator.
Construct the following function with logic gates : Y = (A + B) (C + D + E) (F + G + H + I) (JKL)
Explain the term critical magnetic field in a superconductor. How does the critical magnetic field vary with temperature in Type-I and Type-II superconductors ? What is Meissner effect ?
What are called intrinsic and extrinsic semiconductors ?
Explain the operation of NOR gate with a logical diagram and truth table. Show how NOR gate can be used as Universal gate.
Discuss the four basic types of fundamental interactions in nature and compare them.
Describe the quark model. Obtain the quark composition of baryons and mesons.
Obtain the ground-state wave function, depth of potential and range of nuclear force in deuteron and discuss. Also prove that no bound state exists for l \neq 0.
Discuss the shell model of the nucleus. What are its merits ?
Compute the density of a typical nucleus and find the resultant mass, if we could manufacture a nucleus with a radius of 1\text{ cm}.
What is kinematics of nuclear reaction ? What is the Q-value and its significance ?
Distinguish between fluorescence and phosphorescence in electronically excited molecules.
Explain Russel Saunders coupling. Discuss the summation rules for orbital angular momentum, spin angular momentum and total angular momentum quantum numbers.
State the postulates of Bohr regarding his atom model. Obtain the expressions for the radius and electron-energy of the n^\text{th} orbit. Explain how Bohr's atom model successfully accounts for the hydrogen spectrum.
What is 'multiplicity' ? Give the term symbol for the following cases :
(i) S = \frac{1}{2} \qquad L = 2
(ii) S = 1 \qquad L = 1
