PYQ Bank

Write a short note on Ultrasonic.

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.

Write a short note on Coupled oscillations.

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.

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.

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 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.

Show that the angular momentum of a particle located at position \vec{r} relative to the origin of co-ordinates is given by \vec{l} = \vec{r} \times \vec{p} where \vec{p} is the linear momentum of the particle. Using this result prove that the angular momentum of a system of particles can be expressed as the sum of their angular momentum around the centre of mass and the angular momentum around the origin of a single particle of mass equal to the total mass of the system located at the centre of mass.

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?

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.

A smooth sphere A of mass m and speed u impinges obliquely on a sphere B of mass (M>m) at rest. The velocity of A before collision makes an angle \theta with the line of centres at the time of impact. Show that A is deflected through a right angle if \tan^2\theta=e\frac{M-m}{M+m} where e is the coefficient of restitution.

A \mu meson travels towards the earth's surface from high up in atmosphere with a speed of 0.99\text{ C}. It decays after travelling a distance of 6\text{ km}. In what time does the \mu meson decay as measured by observers in reference frames (i) bound to the earth and (ii) bound to the meson itself.

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}.

Draw the circuit of an emitter-follower and find its voltage gain.

Simplify the following logic function and draw the corresponding logic gates: Y = A.B + B.\overline{C} + \overline{A}.B + \overline{A}.C + \overline{B}.\overline{C} + \overline{A}.\overline{B}.\overline{C} + A.B.C

Explain the basic distinction between a perfect conductor and a superconductor.

Assuming that for a paramagnetic material, the magnetic susceptibility is inversely proportional to temperature in Kelvin, obtain Curie-Weiss law for the paramagnetic phase of a ferro-magnetic material.