PYQ Bank

Show that for forced oscillations amplitude resonance and energy resonance do not occur at the same frequency.

In a biprism experiment the fringe-width with lightly of wavelength \lambda = 5900\text{ \AA} is 0.43\text{ mm}. On introducing a mica sheet in the path of one of the interfering rays the central fringe shifts by 1.89\text{ mm}. If refractive index of mica is 1.59, calculate the thickness of the sheet.

Obtain the intensity pattern due to Fraunhofer diffraction at two parallel slits. Each slit has a width ‘a’ and the separation between the slits is d. How many interference fringes will appear in the central diffraction maximum, it d = 4a?

Write a short note on Fourier transformation.

A left circularly polarized beam of light (\lambda = 6000\text{ \AA}) is incident on a quartz crystal (Optic axis parallel to the surface). Find the state of polarisation of the emergent beam. (Thickness of quartz crystal = 2.3 \times 10^{-5}\text{ m}, \mu_e = 1.5538, \mu_o = 1.5444)

A body of mass m supported by a spiral spring causes an extension of d is the spring. The body is set in vertical oscillations of small amplitude. Find an expression for the periodic time of the oscillations.

A satellite is launched into a circular orbit close to the surface of the earth. Fine an expression for the additional velocity that has to be imparted to the satellite to overcome the gravitational pull.

State Kepler’s laws and prove that for elliptical orbits the square of the period of a satellite is proportional to the cube of the semi-major axis.

Write a short note on Michelson - morley experiment.

In the relativistic region, compare the relative increase in velocity with the relative increase in energy of a particle.

The density of gold in its proper frame of reference is 19.3 \times 10\text{ kg/m}^3. Determine its density is a frame of reference where its velocity is 0.9 c. c is velocity of light in free space.

Determine the speed of an electron which has kinetic energy 1\text{ MeV}. The energy equivalent to the rest mass of an electron is 0.51\text{ MeV}.

The distance between the centres of oxygen and carbon atoms in a carbon monoxide molecule is 1.2\text{ \AA}. Determine the position of the centre of mass of the molecule relative to carbon. (Assume atomic masses of carbon and oxygen as 12 and 16 respectively.)

The potential energy of a particle is given by U = a \cos \alpha x Obtain the positions of stable equilibrium.

A stream of liquid of density \rho and speed v is directed against a plane surface at an angle \theta with the normal to the surface. After striking the surface the liquid spreads over it. Find the pressure on the surface.

Distinguish between stream-line motion and turbulent motion. Hence define Reynold’s number. A sphere of radius 0.1\text{ cm} moves through glycerine. A laminar flow is observed when the velocity of the sphere does not exceed 15\text{ cm/s}. At what minimum velocity of a sphere of radius 5\text{ cm} will the flow in water become turbulent? Viscosity coefficient for glycerine \eta_{\text{gly}} = 14\text{ p} and for water \eta_{\text{wat}} = 0.011\text{ p}, and density of glycerine = 1.2\text{ gm/cc}.

Write a short note on Gyroscope.

What are precession an nutation ? Show that the angular velocity of precession \vec{\Omega} is related to the angular momentum \vec{L} and external torque \vec{r} as \vec{\Omega} \times \vec{L} = \vec{r} Assume \Omega \ll \omega.

Explain the construction and working of a p -n junction solar cell.

What is the difference between the frequency spectrum of amplitude modulated wav and frequency modulated waves? Give a circuit for the detection of frequency modulated waves.