Puslapio vaizdai



Heat and Light.

1. (a) Show that if pv=RmT the coefficient of expansion at constant pressure is equal to that at constant volume.

(b) What explanation do you offer for the fact that no gas actually follows this law?

2. (a) Show that the entropy change around any complete reversible cycle is zero.

(b) How do you reconcile this with the fact that all cases of temperature gradient involve an increase in the entropy of the system?

3. If heat be produced by the isothermal compression of a substance, its coefficient of expansion (at constant pressure) is negative.

(a) Establish the quantitative relation involved in the foregoing qualitative statement.

(b) Apply this relation to find the number of calories liberated isothermally per litre of water at 2.5° due to an increase of pressure of one atmosphere.

at 2° 0.99997. Density of water at 3°

Density of water 0.999999.

4. (a) Briefly describe the porous plug experiment.

(b) What information does it yield directly?

(c) Indicate how it is used to obtain the value of a given temperature on the absolute or work scale.

5. (a) What is meant by "fits of easy refraction?

(b) Show that the unmodified corpuscular theory led to a sine law of refraction.

(c) How was this law used against the corpuscular theory?

6. Show that the "law of the extreme path" and the "law of stationary time" are both laws of stationary phase relation.

7. Discuss, mathematically, the diffraction of light past a straight edge.

8. Discuss generally the use of interference bands from white light in the case of

(a) Michelson's interferometer.

(b) Fabry and Perot's standard air films.



Electricity and Magnetism.

(Candidates will write on seven questions only).

1. (a) What is meant by the "total normal induction" over a closed surface?

(b) Establish Gaus' theorem for the case when the charge is outside the closed surface.

(c) A cylindrical shell of infinite length is uniformly electrified. Find an expression for the electric intensity at any point inside or outside the shell.

2. (a) Define coefficient of potential, of capacity, and of induction.

(b) If p21 and 12 are the coefficients of potential of two neighboring conductors, prove that 12-P21

3. (a) Find the potential of a conducting spherical shell due to a unit charge at a point P (a) outside, (b) inside the sphere.

(b) A spherical conductor of 16 cm. radius is charged to a potential of 100 e.s. units. Two insulated conducting spheres of radii 5 cm. and 3 cm. are placed 60 cm. and 72 cm. distant from the charged sphere respectively. Find the total charge which appears on them when (a) they are counected by a fine wire, (b) and then earthed.

4. (a) Describe Faraday's conception of an electric field. (b) Show that, in air, the electric intensity at a point is given by R=4′′N where N is the number of Faraday tubes per sq. cm. cross-section at the point.

5. (a) What are the boundary conditions when Faraday tubes cross from one dielectric to another?

(b) Find the capacity of two parallel plates when a slab of a dielectric is placed between them.

(c) Show that a conductor may be considered as a dielectric of infinite specific inductive capacity.

6. (a) Assuming La Place's law, find an expression for the magnetic intensity at any point along the axis of a circular wire bearing a current of i e. m. units.

(b) Show that the magnetic intensity at the centre of a long narrow solenoid is equal to


where n number of turns of the solenoid per cm. length, and i current in the solenoid in e. m. units.

7. (a) Given that the mechanical force on an element of current in a magnetic field is equal to Hids sin a, find the work done when the element is displaced a short distance parallel to itself, in terms of the number of magnetic tubes cut, and the current.

(b) Hence show that the work done in taking a unit pole around a closed circuit is equal to 4 times the current in the circuit.

8. (a) Describe the construction of a D'Arsonval ballistic galvanometer.

(b) Find the initial angular velocity of the coil when a quantity of electricity passes through it.

(c) Also establish the equation of motion of the coil, taking into account air resistance.

(d) What are the possible solutions and upon what do they depend?




Candidates will write on question 5 and and three of 1, 2, 3, 4.

1. (a) Explain how and why a gyroscope may be used (1) as a compass, (2) to measure the latitude of a place.

(b) A spherical wooden block (mass 10 kilograms, radius 15 cm.) is capable of rotation about a vertical axis coinciding with one of its diameters. A bullet, mass = 2 grams, is fired horizontally, with a velocity of 250 metres per second, along a line whose nearest distance from the axis is 10 cm. If the bullet remains embedded in the block, find the initial angular velocity.

2. (a) What is meant by precessional motion? Explain clearly why it takes place.

(b) A gyroscopic wheel (mass=600 grams, radius =3 cms.) pivoted in the usual way (with three degrees of freedom and in neutral equilibrium when at rest) is set in rotation by pulling a string 60 cms. long, wound round its horizontal axle, with a constant force of 3 kilograms until it is all unwound. Find the resulting velocity of spin.

If a weight of 100 grams is hung at the edge of a "massless" frame at the end of the axle (5 cms. from the centre), find (1) the velocity of precession, (2) the angle of dip at which steady precession takes place.

3. (a) Obtain graphically or otherwise the resultant path of a particle acted on by two simple harmonic motions of equal amplitude, periods in the ratio 1 to 2 and phase difference 90 degrees.

(b) The restoring force acting on a particle displaced from a position of rest is proportional to the displacement. If its motion be damped, show by means of graphs the two ways in which it may come to rest.

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