UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Define quality factor for an A.C. circular and discuss the meaning of electrical resonance in a series LCR circuit. Explain the term sharpness of resonance.

A deuteron of kinetic energy 40 keV is describing a circular orbit of radius 0.6 m in a plane perpendicular to a magnetic induction \vec{B}. Calculate the kinetic energy of a proton that describes a circular trajectory of radius 0.8 m in the same plane with the same \vec{B}.

What was the basis for light to be accepted as an electromagnetic wave ? The \vec{E} vector in a light wave polarised in the (x, y) plane is expressed as \vec{E}(x, y, z, t) = \vec{E}_0 \sin\left[\omega t - k(x + y)\right] Determine the propagation and the polarisation vectors.

Write down the expression for the energy distribution for the black body radiations at temperature T. Show that this expression goes into the Rayleigh-Jeans distribution at one end of the frequency spectrum and the Wiens distribution at the other end.

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?

A thin quartz plate for incident light of \lambda = 6100\ \text{\AA} produces, a phase difference (45/4)\lambda between the ordinary and extraordinary rays. What will be the nature of polarisation of the emergent light when plane polarized light of wavelength 4500\text{\AA} is incident on it.

Write a short note on Ruby laser.

Calculate the minimum plate separation in a Fabry-Perot interferometer to obtain free spectral range of 0.05\text{\AA} in the wave length region 5000\text{\AA}. Calculate also the smallest resolvable wavelength difference for reflectivity of 0.95.

Define dispersive and resolving powers of a plane transmission grating and obtain expressions for the two. Show that the first and second order spectra produced by such a grating will never overlap when the incident light contains wave-lengths in the range 4000\text{\AA} to 7000\text{\AA}.

Stale Huygens principle and use it to establish Snell's law of refraction of light. How does this treatment of refraction differ from that given on the basis of Newton's corpuscular theory?

Distinguish between spatial and temporal coherence of light. What kind of coherence is required for interference and diffraction? Explain why it is possible to produce interference effects using two tuning forks of the same frequency but not by two independent sources of light of the same wavelength.

Explain the terms resolving power and magnifying power of an optical instrument. On what parameter do these physical quantities depend in case of a telescope? For a given re-solving power what is the optimum magnifying power in this case ?

Write a short note on Coupled oscillations.

Write a short note on Ultrasonic.

How is an electron volt conned to other units of energy like the Joule or the org ? Determine the speed of an election of energy 1.3\text{ Mev} assuming its rest energy to be 0.5\text{ Mev}.

A steel ball 1.00\text{mm} in diameter at constant speed of 0.176\text{ cm s}^{-1} in a large vessel filled with oil. Calculate the dynamic viscosity of oil. Given density of steel = 7700\text{ kg m}^{-3} and that of oil = 900\text{ kg m}^{-3}. Deduce the mathematical relation needed for the calculation.

Write a short note on Gyroscope.

A block A of mass 6\text{ kg} is placed on a plane inclined to the horizontal at an angle 30^\circ. It is joined to another block B of mass 18\text{ kg} by means of a massless string going round a pulley. B hangs vertically. The pulley can be approximated as a uniform circular disc of mass 2\text{kg} and radius 10\text{cm}. The string from A to the pulley is parallel to the plane. The kinetic friction coefficient is \frac{1}{3\sqrt{3}}. Calculate the acceleration of B and the tensions in the two segments of the string.

Prove that the path of particle moving in a central force field is a plane curve and that the angular momentum of the particle remains constant in time.

Consider a spiral spring of length L and mass M suspended vertically from a rigid support. A mass m is attached to the lower end of the spring. The mass m is now pulled down through a small distance and is then released. If M and m are comparable describe the motion. What elastic constant of the material of the spiral spring provides the restoring force?