NATURAL PHILOSOPHY.-PART I. The Board of Examiners. Candidates must not attempt more than TEN of the following questions. 1. Define force, impulse, kinetic energy, and explain how they are measured. A bullet weighing 15 grams leaves the muzzle of a rifle with a velocity of 400 metres per second; (a) find the impulse and the kinetic energy it has received; (b) find the mean value of the propelling force on the bullet, supposing the barrel of the rifle to be 1 metre long. 2. Explain how velocities are compounded and resolved graphically. A ship steaming north-east through a current running 4 knots an hour is found after an hour to have made 4 knots due north. Determine the direction of current and the speed of the ship. 3. Describe Attwood's machine and how to use it to verify the formula v2/h = constant. 4. Define elasticity. Distinguish between elasticity of bulk and elasticity of form, and show how this distinction may be made the basis of the classification of matter into solids and fluids. 5. Describe how to test the uniformity of the bore of a capillary tube. If the bore is circular, describe how to determine its diameter. Obtain a formula giving the diameter in terms of the results of experiment. 6. State the principle of Archimedes, and give any method of proving it. A body floats in pure water with one-fourth of its volume above the surface. What fraction of its volume will project above the surface if it be floated in a liquid of specific gravity 1·35 ? 7. A quantity of gas collected in a graduated tube over mercury measures 578 cubic centimetres; the level of the mercury in the tube is 48 millimetres above that in the dish which is open to the atmosphere; the barometer reads 750 m.m., and the temperature is 20° C. Calculate the volume of the gas at 0° C. and 760 m.m. pressure. 8. Define the quantities unit of work and unit of heat, and describe how to determine how many units of work are equivalent to one unit of heat. 9. Explain, and illustrate by a figure, the formation of the image of an object by a convex mirror. Explain clearly how it is we see the image in its apparent position. 10. How would you show that the poles of a good bar magnet are not situated at its ends but near them? How would you operate so as to make both ends of a steel knitting needle north poles and the middle of it a south pole, and how would you prove experimentally that you had succeeded? 11. A delicate gold-leaf electroscope is placed inside a wire gauze enclosure, its plate being connected to the gauze, and the whole apparatus placed on an insulating stool. What will be the effect on the gold leaves if an electrified body be brought up to and made to touch the gauze ? What fundamental electrical principle does this experiment prove? Describe other experiments to prove the same principle. 12. What do you understand by electro-magnetic induction? Describe the apparatus used, and the method of using it, for proving the fundamental laws of electro-magnetic induction. NATURAL PHILOSOPHY.-PART II. The Board of Examiners. No candidate is to attempt more than TEN questions. 1. Assuming that the resistance to motion is lbs. weight per ton of engine and train where v 2. Prove that a spherical shell of gravitating matter exerts no force on a particle placed at an internal point. Ꮓ * 8. Describe the apparatus used and the results obtained by Andrews in his researches on the forms of the isothermals of carbonic dioxide. 4. A cylinder of glass whose coefficient of linear expansion=0000085 weighs 6.787 grams in air, 4.222 grams in water at 4° C., 4·261 grams in water at 60° C., and 4·323 grams in water at 100° C. Determine the volumes occupied by 1 gram of water at 60° and at 100°, and the mean coefficient of expansion of water between 4° and 60°, and between 60° and 100°. 5. Describe with full experimental detail how you would test the accuracy of Newton's law of cooling. 6. Assuming the inverse square law for electrical action and the usual definitions for potential and capacity, prove completely the expression for the capacity of a sphere. Obtain also the expression for the capacity of a condenser made of two concentric spherical conductors. 7. Two points, A and B, are connected in parallel by two wires, and a given constant current passes through them from A to B. Show that if this current divides itself between the wires so as to satisfy Kirchhoff's second law less heat will be generated in them than if it divided itself in any other ratio. 8. A condenser is charged by a standard cell on open circuit, and discharged through a ballistic galvanometer which gives a swing of 300 divisions. The condenser is again charged by the same cell, the terminals of the cell being now joined by a resistance 10,000 ohms. On discharging through the ballistic galvanometer a swing 250 divisions is observed. What is the internal resistance of the cell? 9. Describe how sound is transmitted through the air. Two exactly similar tuning forks are placed at a distance from each other, the line joining them being perpendicular to the planes of vibration of their prongs. Describe fully the condition of the air in the line joining the forks when they are kept vibrating steadily. 10. Describe how to compare the velocities of sound in different gases. 11. Describe how to construct an achromatic (q.p.) prism of two materials. Prove the relation which gives the ratio of the angles of the two parts in terms of the optical constants of their materials. 12. Prove that if d, be the minimum deviation and d2 the maximum deviation that can be produced by a prism of angle a on a ray for which the refractive index is μ μ, then sin (a + da). |