A singly charged positive ion is accelerated through a potential difference of one \text{kV}, and the ion passes through a uniform magnetic field of B=0.2\text{ Wb/m}^{2} and consequently gets deflected through a circular path of radius 0.1\text{ metre}. Find out the mass number of the ion.

State Kirchoff's laws for the distribution of currents (a) in the usual form for steady currents and (b) in a form applicable to alternating current networks. Discuss the method for comparing inductances by using Maxwell's bridge. State the disadvantages of the method.

A 220\text{ volt}, 50\text{ cycle}, supply is connected to a circuit containing a resistance of 20\text{ ohms} in series with a 100\mu\text{F} capacitor. Determine the current and the phase.

The diameter of the central zone of a zone-plate is 2.3\text{ mm}. If a point source of light (\lambda=589.3\text{ nanometer}) is placed at a distance of 6\text{ metre} from it, calculate the position of the first image.

The above expression shows that, for given W, \theta and \lambda, the resolving power is independent of number of grooves on the grating. Why do most diffraction gratings have several hundred grooves per mm?

Write a short note on Spatial and temporal coherence.

Two express trains travelling at 10\text{ km/hour} are meeting each other while one of them is whistling. If the frequency of the note is 800\text{ Hz}, find the apparent pitch as heard by an observer in the other train after they passed each other. Velocity of sound in air = 340\text{ ms}^{-1}.

Calculate the rate of energy dissipation by a damped harmonic oscillator, in the weak damping limit with \omega_o \tau \gg 1, so that \omega=\omega_o. Symbols have their usual meanings.

If two pipes one closed at one end and the other open at both ends, have fast overtones of the same frequency, what is the ratio of their respective lengths?

A thick wire of mass per unit length m, density p, and Young’s Modulus E, is stretched between two supports and has a tension T. Obtain from first principles an expression for the velocity of longitudinal waves in the wire. Write down the equivalent expression for velocity of transverse waves in the same wire.

Write a short note on Holography.

A beam of linearly polarised light is changed into circularly polarised light by passing it through a slice crystal 0.003\text{ cm} thick. Calculate the difference in refractive index of two rays in crystal assuming this to be minimum thickness that will produce the effect and that the wavelength of light is 6 \times 10^{-7}\text{ m}.

Show that the resolving power of a diffraction grating used with light of wavelength \lambda at normal incidence is W \sin \theta/\lambda, where W is the total width of the grating \theta the angle of diffraction.

Show from the Lorentz transformation that two events (t_1=t_2) at different points (x_1 \neq x_2) in reference frame S are not in general simultaneous in reference frame S which is moving in the + direction with the constant velocity V with respect to S.

Two objects (M_1=2\text{ gm}: M_2=5\text{ gm}) process Velocities V_1= 10\hat{x}\text{ cm/sec}, V_2 = 3\hat{x}+ 5\hat{y}\text{ cm/sec} just prior to a collision during which they become permanently attached to each other. What is the final momentum of combination of the laboratory system ?

Write a short note on Motion of rocket under constant force field.

What is the recoil energy in electron-volts of a nucleus of mass 10^{-23}\text{ gm} after emission of x-ray of energy 1\text{ MeV}?

What is understood by the term ‘Coriolis force’? Obtain expressions for velocity and acceleration of a particle in rotating coordinate systems.

Water is flowing through a horizontal pipe line of varying cross-section. If the pressure of water equals 2\text{cm} of mercury at a point where velocity of the flow is 32\text{ cm/sec}. What is the pressure at another point where velocity of flow is 40\text{ cm/sec}?

What is the angular momentum (referred to the centre of the orbit) of a satellite of mass M, which moves round the earth in a circular orbit of radius r? The result is to be expressed in terms only r, G.M, and M_e (the mass of the earth).