Physics Optional – Other Questions Outside the Present Syllabus (1995–2026)

These 20 questions from UPSC Physics Optional papers (1995–2026) fall outside the present syllabus of their paper – mostly from papers set on the older syllabus. We keep them here for completeness.

Each question ends with a code such as [2024/15m/3b] – the year, the marks, the word limit (where UPSC set one) and the question number in the paper.

Paper I

11 questions

1. Write down the Lagrangian of a free particle in rectangular cartesian coordinates. Identify all the cyclic coordinates. Show that the constants of motion obtained from the equations for the considered form of the Lagrangian are not exactly the same as those which follow from the concept of a free particle. [2007/20m/1a]

2. What is Hamilton’s principle? Obtain Lagrange’s equations of motion with its help for a conservative system. [2006/25m/2a]

3. What are constraints of motion? Explain with examples the holonomic and non-holonomic constraints. Discuss critically how can one overcome the limits of constraints by introducing generalised coordinates. [2005/20m/2b]

4. A particle moves in space with the Lagrangian $L=1/2m({\dot{x}}^2+{\dot{y}}^2+{\dot{z}}^2)-V+A\dot{x}+B\dot{y}+C\dot{z}$ where A, B, C are given functions of x, y, z. Find the corresponding Hamiltonian in terms of coordinates and momenta. [2004/20m/1a]

5. Write the Lagrange’s equation for a system of particles which is acted upon by Conservative forces. What is a cyclic coordinate? Show that the generalized momentum conjugate to a cyclic coordinate is conserved. [2003/20m/3a]

6. A system with 2 independent coordinates $x_1$ and $x_2$ has the following Lagrangian $L=\frac{1}{2}\frac{{\left(x_1\right)}^2}{\alpha +\beta x_2}+\frac{1}{2}{\left(x_2\right)}^2{\left(x_2\right)}^2-\gamma x_2$ $\alpha$, $\beta$, $\gamma$ being constants. Obtain the Lagrangian equation of motion. [2001/20m/1d]

7. Consider a resonant cavity of volume V of a container to which a neck of area of cross section a and length $l$ is attached. Show that the product of the square of resonance frequency n and volume V is constant. Comment on the correction needed to the derived relation between $n^2$ and V. How will you determine this correction? [1998/20m/5c]

8. Ultrasonic. [1998/20m/8e]

9. Fourier transformation. [1996/20m/8f]

10. Fourier transformation. [1995/20m/8d]

11. Fourier transformation. [1995/20m/8f]

Paper II

9 questions

1. In an almost pure thick aluminium sheet, there are 0.19 atomic percent of copper at the surface and 0.18 atomic percent at a depth of 1.2 mm from the surface. Calculate the flux of the copper atoms from the surface at 550 °C, if the diffusion coefficient of copper in aluminium at this temperature is $5\cdot 25\times {10}^{-13}{m}^2{s}^{-1}$. Given, Al FCC with lattice parameter, $a=4\cdot 05$ Å. [2020/10m/5d]

2. Why is population inversion in general not possible in a two-level laser system? Explain it. [2019/10m/1d]

3. If K, L and M energy levels of platinum are approximately 78, 12 and 3 keV, respectively, below the vacuum level, calculate the wavelengths of $K_{\alpha }$ and $K_{\beta }$ lines. [2015/10m/1e]

4. How is frequency modulation advantageous compared to amplitude modulation? Still, why are the video signals transmitted by television stations amplitude modulated? [1999/20m/4b]

5. Describe the broad features of characteristic X-rays spectra and discuss how these have been accounted for. [1998/30m/7a]

6. 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? [1998/30m/7b]

7. Explain the origin of continuous X-rays. Compare the phenomenon with photoelectric effect. [1997/20m/5b]

8. Derive the expression for the frequency spectrum of a carrier wave of frequency $f_c$ which is amplitude modulated by a frequency $f_m$. A certain transmitter radiates 9 kW of power when the carrier wave is unmodulated and 10.12 kW power when the carrier wave is sinusoidally modulated. Calculate the modulation index. [1996/20m/1d]

9. Draw the block diagram of a superhetrodyne radio receiver and explain the function of local oscillator. [1995/30m/4b]

« Previous: Solid State Physics, Devices and Electronics

Back to: Physics Optional PYQs – Topic-wise

Last updated: 30 October 2026