Search, filter, and study UPSC Civil Services & IFoS Physics past year questions with rigorous derivations, formulas, and step-by-step solutions.
Explain the precession of a spinning top and show that precssional angular velocity is independent of the angle of inclination. A top is spinning with 20 rev/s about an axis inclined at 30^\circ with the vertical. Its radius of gyration is 5 cm. The centre of mass is \pi cm from the pivot point. Calculate the frequency of precession.
Distinguish between elastic and inelastic collision. Find the minimum distance an \alpha-particle with kinetic energy of 0.4 Mev can approach a stationary but free Lithium nucleus in a head-on collision.
How do we infer the law of conservation of linear momentum from Newton's laws of motion? A stationary bomb explodes and on explosion, it fragments into three parts. Two of these part which are of equal masses fly apart perpendicular to each other with a velocity of 60 m/s each. The third part has a mass four times the other two. Find the magnitude and the direction of the velocity of the third part.
Discuss the Reynolds number for describing the stability of fluid flow, Air streams horizontally across an aeroplane wing of area 4\text{ m}^2 and weighing 300 kg. The air speed is 60 m/s and 40 m/s over the top surface and under the bottom surface respectively. Find (i) the lift on the wing and (ii) the net force on it, given that the density of air is equal to 1.293\text{ kg/m}^3.
Prove that the expression x^2+y^2+z^2-c^2t^2 is invariant under Lorentz transformation.
Describe the set-up of Michelson-Morley experiment. Why was a fringe shift expected in it? How are its negative results understood?
What is the photovoltaic mode of operation for a photo-diode? Describe the construction and working of a silicon solar cell.
Distinguish qualitatively between dia-, para-, ferro-, antiferro- and ferrimagnetism. How is the weak and temperature independence paramagnetism of metals explain?
Simplify the following logic function and draw the corresponding logic diagram:- Y = (A+B).(A + C).(B+C)
If E_0 is the peak value of the input voltage V_{in} calculate the output voltage V_{out}.
Explain the working N-P-N transistor. Derive expression for the current and voltage gains.
What is the basis of thermonuclear fusion? Estimate the order of temperatures required for promoting the fusion reaction of lighter nuclei. Calculate the Q-value of the proton-proton cycle. 4 {}_1^1 H \rightarrow {}_2^4 He + 2 {}_{+1}^0 e + Q.
In nature, we have basically four kinds of forces in the following order of increasing interaction strength: (i) Gravitational (ii) Weak (iii) electromagnetic (iv) Nuclear or strong Comment on their spatial dependence and give their strength in terms of dimensionless coupling constants.
Describe the broad features of characteristic X-rays spectra and discuss how these have been accounted for
Draw the energy level diagram showing the Zeeman splitting of {}^2P_{1/2, 3/2} and {}^2S_{1/2} levels in a weak magnetic field. Give the selection rules and the resulting transitions, between the sub-levels. Does the magnetic interaction lift the degeneracy of the level only partially or wholly?
Calculate the force constant for the coupling between H and Cl, given that the fundamental frequency of H^1 Cl^{35} molecule is 8.7 \times 10^{13}\text{ Hz}. Assuming the force constant of H^2 Cl^{35} to be the same as that of H^1 Cl^{35}, calculate the vibration frequency of H^2 Cl^{35}
The atomic number of Na is 11. (i) Write down the electronic configuration for the ground state of the Na atoms (ii) Give the standard spectroscopic notation for the ground state. (iii) The lowest frequency in the absorption spectrum of Na is a doublet. What are the spectroscopic designations of the pair of energy levels to which the atom is excited as a result of this absorption process? (iv) What is the mechanism responsible for the splitting between the pairs of energy levels? (v) Does the level corresponding to the higher value of j lie lower or higher?
Explain why in optical absorption discrete lines are observed but X-ray absorption shows continue with edges. Why the emission and absorption spectra of X-rays are not identical ?
An infinite well potential is V(x) = \begin{cases} 0, & -a/2 < x < a/2 \\ \infty, & x < -a/2, \quad x > a/2 \end{cases} Solve the time independent Schrodinger equation and find the closed form expressions for the eigenvalues and eigenfunction of potential. Give a schematic representation of the first three energy levels and corresponding wave functions and probability distribution functions. Show that the zero-point energy is in accord with the uncertainty principle.
Derive an expression for the Compton shift (\Delta\lambda) and show that it is independent of the wavelength of incident radiation. Establish parallelism between Compton and Raman scattering