Search, filter, and study UPSC Civil Services & IFoS Physics past year questions with rigorous derivations, formulas, and step-by-step solutions.
In a series L–C–R circuit connected to an alternating constant voltage source the current amplitude is (1/n) times the amplitude at resonance at frequencies w_1 and w_2. Obtain an expression for its quality factor at resonant frequency.
Two inductance coils hang inductances L_1 and L_2 and negligible resistances are connected in parallel. The coils have a mutual inductance M. Obtain an expression for the effective inductance of the combination.
The frequency of applied voltage in a cyclotron is 1.2 \times 10^7\text{ Hz}. Find the magnetic field strength when protons are to be accelerated. If the radius of dees is 0.5 m, what is the energy of the accelerated protons ?
In the given circuit the output voltage v_0 at time t second after closing the key K is 1 volt. Calculate the rate of change of current in the inductance coil at this moment.
What are the essential conditions for observing the interference of light? Two coherent sources with intensity ratio 4 : 1 interfere. Find I_{\text{max}} / I_{\text{min}}.
Why an extended source is necessary to see colours in a soap-film ? Non-reflecting surfaces are made by coating very thin films of a transparent material. Find the maximum thickness of such thin coatings given that \lambda = 5.5 \times 10^{-5}\text{ cm} and \mu = 5/4.
Sodium light is incident normally upon a plane transmission grating having 5000 lines/cm. Calculate the angular separation of the D_1 and D_2 lines in the first order spectrum. As this angular separation is very sexy small, how can one magnify it 10 times ? (Given : \lambda_{v1} = 5690\text{ \AA} and \lambda_{v2} = 5896\text{ \AA})
Differentiate between Fresnel and Fraunhoffer diffractions. How can one explain the Fresnel diffraction pattern due to a straight edge?
Give Rayleigh's criterion for resolution. Why telescopes with larger objectives are better? The objective of the telescope at St. Palomer has a diameter of 5.08 m. What is the least distance on Moon which could be resolved by it? (Given distance of moon from the Earth = 3,84,000 km and \lambda = 5890\text{ \AA}).
Calculate the peak values of \vec{E} and \vec{B} for a laser beam of power 2 \times 10^{10}\text{ W} and radius 0.1 mm.
Write a short note on Forced oscillations.
Write a short note on Holography.
What are damped oscillations ? Obtain the differential equation for damped oscillations and write its possible solution. Explain with corresponding sketches, when there can be very heavy damping, critical damping and weak damping.
The equation of a one-dimensional propagating harmonic transverse wave is given by: y = 8 \sin 30\pi \left(t - \frac{x}{240}\right) \text{meter} Find the resultant wave formed by the superposition of the incident and the reflected waves from a rigid end. Also determine the amplitude of stationary waves formed at x = 2\text{ meter}. What will be the distance between consecutive nodes ?
A short-focus lens is used to focus a laser beam of wavelength 6328 \AA. If the beam width is comparable to the focal length of the lens, calculate the area of cross-section of the region of focus.
Explain why a two-level system is not adequate for laser operation. Draw the essential parts of a ruby laser and explain the working principle with the help of an energy level diagram.
Write a short note on Applications of Bernoulli's equation.
Write a short note on Geostationary satellites.
Consider the motion of a rocket in a gravitational field and derive an expression for its final velocity when the fuel burns at a constant rate till it is fully consumed.
Starting from the definition of angular momentum of a single particle, obtain an expression for the angular momentum of a rotating rigid body. Hence, discuss the time derivative of the angular momentum and deduce the law of conservation of momentum.