Search, filter, and study UPSC Civil Services & IFoS Physics past year questions with rigorous derivations, formulas, and step-by-step solutions.
Calculate the magnetic moment of a coil having 100 turns, each of area 10\text{ cm}^2 carrying a current of 1\text{ mA}, flowing for 1\text{ ms}. The coil is placed in a magnetic field of 0.5\text{ kg} which is perpendicular to the magnetic moment. Calculate the torque acting on the coil and the angular momentum transferred to it.
The self inductance of primary and secondary coils of a R.F. transformer is 10\text{ mH} each. When the coils are connected in series self resonating frequencies are 132.6\text{ kHz} and 108.3\text{ kHz}. Calculate the mutual inductance between the coils and the winding capacitance.
Obtain the characteristic impedance of the vacuum. Derive the expression used.
An alternating voltage, v = V_0 \sin (\omega t + \phi) is applied to a series RL circuit through a switch. Find the sum total of the transient and steady currents. Find the conditions when transient current becomes
(i) zero, and
(ii) maximum
Write down Maxwell's equations in free space and hence show that the phase velocity of the electromagnetic wave is equal to the velocity of light in free space.
What is spatial coherence ? Considering Young's two slit experiment, prove that the distance between the slits must be sufficiently less than (\lambda/\theta) for obtaining fringes of good contrast. \lambda is the wavelength of light used and \theta is the angle subtended by the source at the slits.
What is a quarter plate? A phase retardation plate of quartz has a thickness 0.1436\text{ mm}. Calculate the wavelength in visible region for which this plate will act as a quarter for plate. The refraction indices of quartz for ordinary and extraordinary rays are 1.5443 and 1.5533 respectively.
A 3 MW laser beam which has a diameter of 1\text{ cm} is foccussed by a lens of focal length 5\text{ cm}. The wavelength of laser is 10,000\text{ \AA}. Calculate the intensity of the focal plane of the lens.
Why does a soap film appear coloured when is viewed by reflected white light? A thin film is illuminated by sodium light of wavelength 5900\text{\AA}. Its refractive index is 1.42. Calculate its minimum thickness so that it appears dark in reflected light.
Write a short note on He-Ne laser.
A plane transmission grating has 6000 lines per cm. Determine the angular separation between the two lines of sodium of wavelengths 5896\text{ \AA} and 5890\text{ \AA} in the second order spectrum. If the width of the grating is 2.5\text{ cm}, will these lines be resolved?
Write a short note on Phase and group velocities in dispersive media.
A uniform rope of mass M and length L is hanging from a rigid support. A transverse wave travels along the rope. Calculate the speed of the wave at a distance x from the free end the time taken by the wave to travel the whole length.
The amplitude of damped oscillator of frequency 300\text{ Hz} reduces one-tenth of its initial amplitude after 3000 oscillations. Calculate the damping constant and the time in which its energy will reduce to one-tenth of its initial energy.
Give the concept of Fresnel's half period zones. Describe the salient features of Fresnel's diffraction pattern due to a straight edge, showing the intensity distribution. How are these features explained?
In a hydrogen atom for the 2\text{p} \to 1\text{ s} transition the probability per unit time is 6 \times 10^8\text{ s}^{-1}. Calculate the angular frequency of the emitted photons and the order of Einstein's coefficient \text{B}_{21}.
Obtain the relativistic transformation relation for density in inertial frames. Why is the equivalent energy corresponding to 1 amu of mass?
Moving in a closed elliptical orbit, Halley's comet goes round the Sun once every 75 years. At its point of closest approach its distance from the Sun is 8.9 \times 10^7\text{ km}. If mass of the Sun is 2 \times 10^{30}\text{ kg}, what will be the greatest distance of the comet from the Sun ?
A particle is moving under a central force field. Obtain the equations of motion and prove that in such a field the areal velocity of the particle remains constant.
Distinguish between streamline and turbulent motion. Define Reynolds number. When a sphere of radius 1.2\text{ mm} moves in glycerine, the laminar flow observed if the velocity of sphere does not exceed 0.23\text{ ms}^{-1}. At that minimum velocity of sphere of radius 5.5\text{ cm} will the flow in water become turbulent? The viscosities of glycerine and water are 11.9\text{ P} and 0.011\text{ P} respectively. The density of glycerine is 1.2 \times 10^{-3}\text{ Kg/m}^3.