What do you understand by streamline motion and critical velocity of a viscous liquid through a capillary tube. Capillaries of lengths l, 2l and \frac{l}{2} are connected in series. Their radii are r, \frac{r}{2} and \frac{r}{3} respectively. If the streamline flow is maintained and the pressure across the first capillary is P_1, deduce the pressures across the second and the third capillaries.
Show that the Bulk modulus K, Young's modu- lus Y and Poisson's ratio \sigma are connected by the relation K = \frac{Y}{3(1 - 2\sigma)}.
A force field is given by \bar{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 ?
Derive an expression for the radial and transverse components of the acceleration of a particle moving in a plane. What inferences would you draw regarding the angular momentum if the transverse acceleration is zero ?
Draw the device structure of a p-n junction solar cell and explain how the light energy is converted into electrical energy. Define the 'short-circuit current', open-circuit voltage' and 'efficiency' of a solar cell.
Explain the difference between n-p-n and p-n-p transistors. Give their device structure and biasing circuits. Draw a circuit for a single-stage common-emitter amplifier.
Discuss briefly the concept of effective mass in semiconductors and explain the significance of negative effective mass.
What is Josephson effect? Discuss briefly DC and AC effects. Give some practical applications of Josephson junctions.
Show that a lattice cannot have a five-fold rotational symmetry. However, some solids appear to exhibit this rotational symmetry. Explain briefly how this can be done.
Give the Boolean expression and the truth table for an XOR gate. Why are NAND gates called universal gates ? Realise OR and XOR gates employing only NAND gates.
Simplify the equation: Y = [A \bar{B} (C + BD) + \bar{A} B C] using Boolean algebra. Give the logic circuit for the equation before and after the simplification.
Explain the working of a phase-shift oscillator. Draw the circuit diagram of a phase-shift oscillator using either a transistor or an op-amp. What are the conditions which must be satisfied to achieve stable oscillations ? Calculate the frequency of oscillations for R = 10\ \Omega and C = 0.01\ \mu\text{F}.
State the quantum numbers I_3, Y and S for the uds quarks and antiquarks. Which combination of these leads to the formation of (1) proton and (2) neutron ?
Write down the Bethe-Weizsacker semi-empirical mass formula for a nucleus. Explain the significance of each term occurring in it. Discuss the stability of a nucleus against \beta-decay. What is the effect of pairing term on stability?
What are mirror nuclei ? How does the charge independence of nuclear force emerge from this concept?
A star converts all its hydrogen to helium, achieving 100% helium composition. It then converts the helium to carbon via the reaction {}^{4}_{2}\text{He} + \text{He} \rightarrow {}^{12}_{6}\text{C} + 7.27\text{ MeV} The mass of the star is 5 \times 10^{32}\text{ kg} and it generates energy at the rate of 5 \times 10^{30}\text{ W}. How long will it take to convert all helium to carbon at this rate ?
Give some characteristic properties of strange particles which distinguish them from non-strange ones. Write the Gell-Mann-Nishijima relation. How is it used for the classification of elementary particles?
(i) Calculate the Q-value of the reaction {}^9_4\text{Be} (^4_2\text{He}, n) ^{12}_6\text{C} Given \text{Mass } (^9\text{Be}) = 9.012183\text{ u} \text{Mass } (^4\text{He}) = 4.002603\text{ u} \text{Mass } (^{12}\text{C}) = 12.000\text{ u} Write down the nucleonic configuration of {}^{7}\text{Li}, {}^{12}\text{C}, {}^{17}\text{O} and {}^{27}\text{Al} in the ground state of the nuclear shell model and hence calculate the corresponding ground state angular momenta and parities. How do the observed ground state angular momenta and parities agree with those predicted on the basis of the shell model ?
Describe Stern-Gerlach experiment. Explain how it demonstrates the discrete nature of the magnetic moment of an atom.
(i) What is Lamb shift ? Has it been observed in any atom other than hydrogen? (10) (ii) How does the 21 cm hydrogen line originate? Comment on its astronomical applications. (10)
