FACULTY OF ARTS.

PRELIMINARY EXPERIMENTAL HONOUR PHYSICS.

(Candidates will answer six questions only).

1. (a) Define moment of inertia, radius of gyration. (b) A soild cylinder rolls down an inclined plane 20 ft. long, making an angle of 30° with the horizontal. Find (1) the time it takes to roll down, (2) its total kinetic energy at the bottom.

2. (a) Define centre of oscillation, centre of suspension, centre of percussion.

(b) A uniform rod, of length 2a, fixed at one end and capable of motion in a vertical plane, is hanging freely under the action of gravity, and being struck perpendicular to its length, rises until it is in a horizontal position. Find the impulse of the blow if there is no strain at the fixed point.

3. What is meant by centripetal acceleration?

Explain the effect of the rotation of the earth on the apparent weight of a body, and show that in the northern hemisphere the rotation of the whirl in a cyclone is in an anti-clockwise direction.

4. (a) What is meant by precession? Make reference to a gyroscope and to the astronomical precession of the equinoxes.

(b) In the case of a spinning gyroscope, if we hurry on the precession the centre of mass of the system rises. What is the fundamental reason of this?

5. (a) Define pure torsion, neutral axis, bending

moment.

(b) Prove that the centre of mass of a section of a loaded beam lies in the line in which the neutral surface cuts this section.

or

(b) If a solid rod of length 7, of radius a, and of material whose coefficient of rigidity is n, is twisted through an angle 0 by the application at one end of an external torque L, the other end being fixed, establish the condition of equilibrium.

6. Make use of Bernoulli's theorem (1/2pv2 +gph+ pa constant) in the following:

(a) A siphon is arranged with its longest leg 6 ft. below the surface of the water in a tank. (1) If the level of the water in the tank is kept constant, find the velocity of efflux of the water from the siphon. (2) If the sectional area of the siphon at the highest point is one half that at the open end, find the velocity of the water at the highest point.

(b) Explain the cuts and curves of a tennis ball.

7. (a) The surface of a liquid possesses peculiar properties. Mention one or two examples of this and explain why this is what we should expect from theoretical considerations.

(b) Explain the necessity of nuclei for the formation of water drops. How could you show this by experiment?

8. (a) Establish Boyle's law on the basis of the kinetic theory of gases, stating clearly what assumptions you make.

(b) If the density of hydrogen at o°C and standard pressure is 0.00009, calculate the mean square velocity of its molecules.

9. (a) What are adiabatic and isothermal lines? Give the equation of each.

(b) A certain mass of dry steam expands adiabatically from a volume v to 2v. If the initial temperature of the steam is 400°C., find the fall in temperature.

y for steam=1.3.

FINAL HONOUR PHYSICS.

Heat.

1. Two gases composed of different kinds of molecules (all alike in each gas), are mixed. Show that when equilibrium is reached that the mean kinetic energy is the same for each kind of molecule.

2. Assuming that the probability that the components of the velocity of a molecule lie between limits u and u+du, v and +d, and w and w+dw, is given by a function of the form (u) du, or (v) dv, etc., show how Maxwell determined the form of the function

.

3. Show that for a monatomic gas the ratio of the specific heats is 5/3. Why does this ratio become smaller for other gases?

4. Show that a field of force will cause a gravitation of molecules in the direction of the field, and find the expression for the pressure at any point in the case of a gravitational field.

5. Discuss briefly Boltzmann's H theorem, stating its object, general method and results.

6. Explain fully the meaning of the constants H and K in Laplace's equation for molecular pressure.

FINAL HONOUR PHYSICS.

Dynamics I.

1. Show how to find the components of the velocity and acceleration of a particle in a plane in terms of rectangular coordinates, polar coordinates, and the tangential and normal directions.

2. Show that the necessary and sufficient condition for equilibrium of a particle or of a system of particles is that the expression for virtual work is equal to zero.

3. (a) Discuss the principle of d'Alembert.

Find the

(b) A heavy chain of length / and mass m hangs freely from its upper end, and is displaced slightly. differential equation of the motion. Do not solve.

4. A particle of mass m is acted upon by a force which is proportional to its distance from the mean position and negative, by a resistance which is proportional to the velocity and a force which is a harmonic function of the time. Find the differential equation of the motion, solve and find the condition for maximum amplitude of vibration.

5. Apply Hamilton's principle to the case of a single particle acted upon by gravity and projected in any direction, and obtain the equations of motion.

6. Show that the cycloidal pendulum is isochronous, and show how it may be realized.

7. Prove the angular momentum principle.