Search, filter, and study UPSC Civil Services & IFoS Physics past year questions with rigorous derivations, formulas, and step-by-step solutions.
When fixed at both ends, a wire under tension of 900\text{ N} and having a linear density 10^{-2}\text{ kg/m} is resonant at the frequency of 420\text{ Hz}. The next higher frequency at which it resonates is 490\text{ Hz}. What is the length of the wire.
Show that Simple Harmonic Motion can he described as the projection on its diameter of a uniform circular motion.
The case of a Simple Harmonic Progressive Wave traversing through a medium is expressed as y = 4 \times 10^{-5} \sin(600\ \pi t + \varphi) Determine
(i) amplitude of vibration of the particles.
(ii) wavelength of the sound wave and
(iii) the phase difference between the particles situated at a distance of 22\text{ cm}. (The sound velocity in the medium is 3.4 \times 10^4\text{ cm/s}).
How does the resolving power of a microscope differ from that of a telescope ? Find the resolving power of an electron microscope that uses 15\text{ Key} electrons, assuming that this is equal to the electron wavelength.
The maximum pressure variation P that the human ear can tolerate in loud sounds is about 28\text{ nt/m}^2. Normal atmospheric pressure is about 100,000\text{ nt/m}^2. Find the corresponding maximum displacement for a soundwave in air having a frequency of 100\text{ cycles/second}. (Take velocity of sound in air as 331\text{ m/sec.} arid density of air = 1.22\text{ kg/m}^3)
Write a short note on Holography.
What is 'Loren & Contraction' ? A spaceship of rest length 100\text{ mm} takes 4\ \mu\text{s} to pass an observer on Earth. What is its velocity relative to the Earth?
An aeroplane makes a complete half circle of 50\text{ m} radius towards left when flying at 200\text{ km / hour}. The rotary engine and the propeller of the plane weigh 400\text{ kg} having a radius of gyration of 30\text{ cm}. The engine rotates at 2400\text{ rpm} clockwise viewing from the rear. Find the gyroscopic couple on the aircraft.
Write a short note on Coriolis force.
Show that the combined effects of translation of the centre of mass and rotation about an axis through the centre of mass are equivalent to a pure rotation with the same angular speed about an axis through the point of contact of a rolling body.
Derive an expression for the mass-energy equivalence using the principle of special relativity.
Ram and Shyam are two skaters weighing 40\text{kg} and 60\text{ kg} respectively. Ram travelling at 4\text{ m/s} meets Shyam travelling at 2\text{ m/s} in opposite direction and collides head-on.
(i) If they remain in contact what is their final velocity ?
(ii) How much kinetic energy is lost ?
Neptune's period of revolution is 165\text{ yr}. What is the average radius of Neptune's orbit in teams of the Sun-Earth distance?
The mass of the Moon is about 0.13 times the mass of the Earth. The distance from the centre of the Moon to the centre of the Earth is 60 times the radius of the Earth. Taking the Earths radius to be 6378\text{ km}. find out the distance of the centre of mass of the Earth - Moon system from the centre of the Earth.
Using Bernoulli's principle indicate how to compute the thrust on a rocket produced by the escape of its exhaust gases.
A top is spinning about its axis of symmetry. If its spin angular momentum is large compared to the change caused by the applied torque the top processes. If it is not spinning, the top would tip over. Show what happens in between, when the top spins slowly. Derive an approximate expression for the angular speed of the precessional motion.
What is Meissner effect? Superconducting tin has a critical temperature of 3.7 K in zero magnetic field and critical field at 0 K is 306 gauss. Determine the critical field at 2K.
Simplify the given Boolean expression and draw the corresponding logic circuit using NAND gates: Y = (\bar{A} + B + C) . (\bar{A} + \bar{B} + C)
How is frequency modulation advantageous compared to amplitude modulation? Still, why are the video signals transmitted by television stations amplitude modulated?
Phosphorous is doped in a silicon wafer. The impurity concentration is 10^{13}\text{ per cm}^3. If all the donors are active calculate its resistivity at room temperature. The mobility of electrons is 1250\text{ cm}^2/\text{V-s}.