Search, filter, and study UPSC Civil Services & IFoS Physics past year questions with rigorous derivations, formulas, and step-by-step solutions.
A meson of rest mass $ \pi $ comes to rest and disintegrates into a muon of rest mass $ \mu $ and a neutrino of zero rest mass. Show that the kinetic energy of motion of the muon is T = \frac{(\pi - \mu)^2 c^2}{2\pi} .
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 ?
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)}.
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.
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.
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.
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.
What is Josephson effect? Discuss briefly DC and AC effects. Give some practical applications of Josephson junctions.
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.
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}.
Discuss briefly the concept of effective mass in semiconductors and explain the significance of negative effective mass.
(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 ?
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 ?
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?
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?
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 ?
What are mirror nuclei ? How does the charge independence of nuclear force emerge from this concept?
(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)
(i) State and explain Franck-Condon principle. (5) (ii) In three separate pairs of electronic states (one ground and another upper state) of diatomic molecules, the average internuclear distances are -