The distance between the centres of the carbon and oxygen atoms in the carbon monoxide gas molecule is 1·130 x 10-10 m. Locate the centre of mass of the molecule relative to the carbon atom. Find the centre of mass of a homogeneous semicircular plate of radius a. Derive the expression for Coriolis force and show that this force is perpendicular to the velocity and to the axis of rotation. What is the nature of this force? Show that the Young's modulus modulus of rigidity n and Poisson's ratio(sigma) are related by the equation Y sigma).
The refractive indices of core and cladding in a step index optical fiber are 1.52 and 1.48 respectively. The diameter of the core is 30 micro meters. If the operating wavelength is 1· 3 micro meters, calculate the V parameter and the maximum number of modes supported by the fiber. Can D1 and D2 lines of sodium light (Lambda D1 5890 A and Lambda D2 5896 be resolved in second-order spectrum if the number of lines in the given grating is 450? Explain.

2.
(a) Four solid spheres C and each of mass m and radius are placed with their centres on the four corners of a square of side b as shown in the figure below: src='./qimages/7928-2a.jpg'>



Calculate the moment of inertia of the system about one side of the square. Also calculate the moment of inertia of the system about a diagonal of the square.

Calculate the percentage contraction in the length of a rod in a frame of reference, moving with velocity 0.8c in a direction parallel to its length and at an angle of with its length. What is the orientation of the rod in the moving frame of reference in case(ii)

A body moving in an inverse square attractive field traverses on elliptical orbit with eccentricity e and period y. Find the time taken by the body to traverse the half of the orbit that is nearer the centre of force. Explain briefly why a comet spends only 18% of its time on the half of its orbit that is nearer the sun.

3. The equation of a progressive wave moving on a string is y 5 sin pi(O.01x 2t). In this equation, y and x are in centimetres and t is in seconds. Calculate amplitude, frequency and velocity of the wave. If two particles at any instant are situated 200 cm apart, what will be the phase difference between these particles?

Explain the principle of induced absorption, spontaneous emission and stimulated emission. Show that the ratio of Einstein's coefficients is given
by

A/B 8*pi*hv3/C3



In Michelson interferometer, 100 fringes cross the field of view when the movable mirror is displaced through 0.029 mm. Calculate the wavelength of
the light source used. Obtain an expression for the resolving power of a grating explaining the Rayleigh's criterion of resolution.

4. A horizontal pipe of non-uniform bore has water flowing through it such that the velocity of flow is 40 cm/s at a point where the pressure is 2 cm of mercury
column. What is the pressure at a point where the velocity of flow is 60
(Take, g =980 cm /s2 and density of water 1 g/c.c.)


Given a proton for which Beeta 0.995 measured in the laboratory. What are the corresponding relativistic energy and momentum? Take, mp 1.67 X 10-24g. Explain the principle of producing polarized light by the method of reflection, refraction and double refraction with the help of neat diagrams. Obtain the conditions for constructive interference and destructive interference in a thin film due to reflected light.

5. In the circuit diagram shown below, the voltmeter reads 50 volts when it is connected across the 400 ohms resistance. Calculate what the same voltmeter will read when connected across the 300 ohms resistance. src='./qimages/7928-5a.jpg'>


(b) In free space, the electric field of electromagnetic wave is given as 120 cos(wt-kx)y V/m. Find the average power crossing a circular area of radius one metre in the yz-plane. The spectral energy curve of the moon shows maxima at 470 nm and 14 micro meters. What inference can you draw from this data? Also calculate the energy density and radiation pressure in both cases. Given, Wien's constant b =2·892 X10-3 m Stefan's constant =5·67X10-8 J m and speed of light c=3x10 power 8 ms-1. m gram of water at temperature T1 is isobarically and adiabatically mixed with an equal mass of water at temperature T2 . Show that the change in entropy is given by

Delta S 2mCp ln(Tav/Tgeo)

where Tav T1 T2/2 and Tgeo Sqrt(T1*T2)
The molecules of a gas obey Maxwell-Boltzmann distribution. Calculate the fraction of molecules of the gas within of the most probable speed at STP. Interpret your result.

6. With the help of a neat diagram, show that the potential due to a dipole at a point is given by
V p*cosQ/4*pi*eo*r2, where p is the dipole moment of the charge distribution, Q is the angle between the line joining the centre of the dipole to the point of interest and the axis of the dipole.
An alternating current varying sinusoidally with a frequency of 50 Hz has an r.m.s. value of 40 A. Find the instantaneous value of the current at 0·00125 second after passing through maximum positive value. Write down Maxwell's equations for linear dielectrics and deduce the equation of continuity. State and prove poynting's theorem.


7. Briefly explain Planck's law of blackbody radiation. Show that Planck's law reduces to Wien's law and Rayleigh-Jeans law at lower and higher wavelength limits respectively. Show that the displacement current between the plates of a parallel-plate capacitor is equal to the conduction current across the conductor. A parallel-plate capacitor is connected to a 240 V AC supply having angular frequency of 300 rad/s. Find the r.m.s. value of the conduction current in the circuit. What is the displacement current between the plates of the capacitor?
Given, C 200 pF. Write down van der Waals' equation of state for n moles of a gas and calculate the temperature at which 5 moles of the gas at 5 atm pressure will occupy a volume of 20 litres.
Given, R=8·31x10 power 7 erg mol-1 K-1 a=1·34x10 power 12 dyne cm4 mol-2 b=31·2cm3 mol-1 and 1atm=1·013x10 power 6 dyne cm-2 .

8. A student is working in a physics laboratory, which is at temperature 27·C, on a sonometer to study formation of stationary waves. The cross-sectional area of the sonometer wire is 0.85 x 10-6 m 2 and a tension of 20 N is applied on it. If the rigid supports are 1·2 m apart and the temperature of the wire drops by 7deg calculate the final tension and fundamental frequency of vibration of the wire. Take, coefficient of linear expansion and isothermal Young's modulus as 1·5xl0-5 K-1 and 2·0xl0 power11 Nm-2 respectively. What do you understand by the term 'phase transition? Using Clausius-Clapeyron equation, show that for first-order phase transitions, vapour pressure decreases exponentially with temperature. You can assume that the vapour behaves like an ideal gas and latent heat remains constant with temperature. Consider a system of N particles and a phase space consisting of only two states with energies 0 and Obtain the expressions for the partition function and the internal energy of the system, if it obeys M-B statistics.
The viscosity in a liquid arises due to friction between adjacent layers. What causes viscosity in a gas? Explain.

(ii) The molecules of a gas obeying Maxwell-Boltzmann distribution move with an average speed of 450 m/s. If the coefficient of viscosity of the gas 11 is 16·6xlO-6 Nsm-2 density of the gas P is 1·25kgm-3 and number density is 2·7 X 10 power 25 m calculate the mean free path and diameter of the gas molecules.