Search, filter, and study UPSC Civil Services & IFoS Physics past year questions with rigorous derivations, formulas, and step-by-step solutions.
The phase velocity of the surface wave in a liquid of surface tension T and density \rho is given by u_p = \sqrt{\frac{g\lambda}{2\pi} + \frac{2\pi T}{\lambda\rho}} Show that the group velocity u_g of the surface wave is given by u_g = \frac{g + (12\pi^2 T) / \rho\lambda^2}{2\sqrt{\left(\frac{2\pi g}{\lambda} + \frac{8\pi^3 T}{\rho\lambda^3}\right)}}
Show that the motion of a classical particle is analogous to the motion of a wave packet, which can be constructed by superposition of a large number of plane waves. Construct such a wave packet and derive an expression for its group velocity.
Discuss the Fresnel diffraction pattern formed by a straight edge using the Cornu's spiral.
Derive the expression for resolving power of a diffraction grating with N lines. Calculate the minimum number of lines in the diffraction grating if it has to resolve the yellow lines of sodium (589.0\text{ nm} and 589.6\text{ nm}) in the first order.
A wave is represented by \Psi_1 = 10 \cos(5x - 25t). Find wavelength \lambda, velocity v, frequency f and the direction of propagation. If it interferes with another was given by \psi_2 = 20 \cos(5x + 25t + \pi/3), find the amplitude and the phase of the resultant wave. (All dimensions are in SI system).
Two spaceships are moving at a velocity of 0.9\text{ c} relative to the Earth in opposite directions. What is the speed of one spaceship relative to the other? (c = \text{velocity of light})
Using the Lagrangian for the system of a planet and the Sun obtain the equation of motion. Use them to get the equations for the orbit.
An observer A sees two events at the same space point (\Delta x = \Delta y = \Delta z = 0) and separated in time by \Delta t = 10^{-6}\text{ s}. Another observer B sees them to be separated by \Delta t' = 3 \times 10^{-6}\text{ s}. What is the separation in space of the two events as observed by B? What is the speed of B relative to A?
Derive the relationship between the impact parameter and the scattering angle for the scattering of an particle of charge +2e by a nucleus of charge +Ze. Calculate the impact parameter for an angle of deflection of 30^\circ if the kinetic energy of the alpha particle is 6 \times 10^{-13}\text{ J}.
Using the rocket equation and its integral find the final velocity of a single stage rocket. Given that
(i) the velocity of the escaping gas is 2500\text{ m/s},
(ii) the rate of loss of mass is. (where m_0) is the initial mass and 0.27 m_0 is the final mass).
(i) Obtain reciprocal lattice to normal BCC lattice. (ii) Describe Josephson junction and the effect. How is it exploited in the formation of a SQUID? Write down the applications of a SQUID. (iii) Distinguish between intrinsic and extrinsic semiconductors. Explain the concept of hole.
(i) Give a qualitative account of BCS theory of superconductivity. (ii) Obtain an expression for conductivity of an intrinsic semiconductor. How does it vary with temperature? (iii) The resistivity of an intrinsic semiconductor is 4.5\text{ ohm-m} at 20^\circ\text{C} and 2.0\text{ ohm-m} at 32^\circ\text{C}. Calculate the energy band gap.
(i) FETs have unique properties which make BJTs not suitable for some important applications. What are these most important FET applications? (ii) Briefly describe FETs as variable resistors.
Explain a solar cell employing its characteristics on output quantity Venus quantities like load current, radiance and temperature.
Combinational switching circuit can perform an addition of the numbers held in two registers. (i) Write down the math table for the addition of two bits. (ii) Write down a Boolean expression for the necessary circuit functions. (iii) Arrive at the Exclusive-OR function. (iv) Draw the logic diagram for the circuit which performs the addition.
(i) What are sequential switching circuits (ii) Describe a simple sequential circuit. (iii) Describe a clocked RS Flip-Flop, (iv) Briefly describe ROMs.
Discuss the significance of Gellmann-Nishijima relation in strange particle production and decay. Give examples in support of your answer. Obtain quark quantum numbers using the modified relation for quarks.
Describe important experimental facts that led Pauli to postulate the existence of neutrino particle.
Discuss briefly the concepts of fission barrier, excitation energy and activation energy on the basis of liquid drop model. Why ^{235}_{92}\text{U} is fissionable by thermal neutrons while ^{238}_{92}\text{U} is not ?
Illustrate with any five examples that production of strange particles conserves strangeness, parity and isotopic spin while their decay violates all these quantities.