Division II.-FLUIDS. INSTRUCTIONS. Read the General Instructions on page 3. Stage 1. You are not permitted to answer more than seven questions. The examination in this subject lasts for three hours. 1. Explain how the velocity of a point moving in a straight line is measured, (a) when it is constant, (b) when it is variable. The acceleration of the velocity of a point is 14 in feet and seconds; find the velocity it acquires when it moves from rest through 56 feet, and the time it takes to describe that distance. (12) 2. State the meaning of the words mass, density, and specific gravity. There are two bodies, A and B; the mass of A is 8 lbs., and it moves with a velocity of 50 feet a second; the mass of B is a ton, and it moves at the rate of 45 yards a minute. Find the ratio of their kinetic energies. (12) 3. Examine the following statement:— An inch of rain means a gallon of water spread over a surface of nearly 2 square feet-or a fall of about 100 tons upon an acre. (10) 4. How are a solid, a liquid, and a gas distinguished from each other ? State how pressure is transmitted through a fluid. A cubical body, edge 2 inches long, is placed in water contained in a cylindrical vessel, which is closed by a piston, whose area is 100 square inches, and which is pressed down by a force of 2,000 lbs.; are transmitted to the cube? what pressures (10) 5. A sphere has a radius 6 inches, and is of weight 35 lbs. If it be suspended by a string and wholly immersed in water, show that the tension of the string is a little less than 2 lbs. 4 ozs. (14) 6. Explain how to determine the pressure at any assigned point of a vessel caused by the weight of the liquid which is in it. Draw a circle and mark the highest and lowest points A and B; also mark points C and D which divide a semi-circle AB into three equal parts. Suppose that the circle represents a spherical vessel full of water, compare the pressures at C, D, B. (12) If AB is 2 ft., find the pressures at C, D, B in pounds per square inch. 7. Explain a method of comparing the specific gravities of air and water. State approximately the result of the comparison. A piece of cork and a piece of lead exactly counterpoise each other in air. If in that state they were placed under the receiver of an air pump, and the air were withdrawn, what effect would be produced on the counterpoise, and why? (14) 8. Draw the Centigrade, Réaumur and Fahrenheit temperature scales side by side, marking the scales at a few intervals from absolute zero up to the boiling point of water. What simple relation connects the three readings of the same temperature with the number 32 ? (14) A given space contains air at pressure p and temperature t and at another time the air is at pressure p' and temperature ; how has the mass of air in the given space changed? (16) 10. Draw a diagram of a safety valve of a boiler and add an explanation. What pressure of steam in a boiler will suffice to raise a circular safety valve which has a diameter inch and is loaded to weigh 2 lbs. ? (12) 11. A silk balloon, 40 feet in diameter, weighing 80 lbs., is filled with hydrogen of specific gravity 0694 (sp. gr. of air 1) and a weight of 2,306 lbs. is required to keep the balloon down. From these data find the weight of air contained in a globe 1 foot in diameter. (16) 12. Explain what is meant by saturation when the word is used with reference to moisture in the atmosphere. Also explain the statement that the pressure of vapour at 27° C. is 1.006 in. of mercury. Define the dew point, and explain the principle on which its determination depends. Stage 2. (14) You are not permitted to answer more than eight questions. 21. A particle moves with uniform velocity round the perimeter of a square; show in a graph the variation in its angular velocity about the middle point of the square. (25) 22. Find the moment of inertia of a rod of uniform density about one end. If such a rod were bent so as to form three sides, AB, 23. A reservoir wall is covered with water to a depth of a feet; find the magnitude, direction, and point of application of the resultant pressure on b feet of its length. If the area under pressure were divided into two equal parts by a horizontal line, find the magnitude, direction, and point of application of the resultant pressure on the lower half. (20) 24. Explain how to find the resultant pressure of a liquid on a plane area. A cone is held, just immersed, in water with its axis horizontal; find the magnitude, direction and line of action of the resultant pressure of the water on the curved surface. N.B.-The centre of pressure of the circular base is five-fourths of the radius below the surface of the water. (20) 25. Define specific gravity and describe a method of measuring it in the case of a substance, such as gunpowder, which it is desired to keep dry during the measurement. Given the specific gravities, s of sea-water and s' of ice; prove that the weight of an iceberg, of which V cubic feet is seen above the water, is where D is the weight in pounds of a cubic foot of water. What is the volume of the iceberg in cubic feet? (25) 26. A body of specific gravity weighed in air by means of Р weights of specific gravity p' appears to have the weight w; show that approximately the true weight of the body is Pa 1 + P -Pa) 10, w, Pa being the specific gravity of air. (20) 27. An isosceles triangular plate, vertical angle 2a, floats vertically with its base horizontal and its vertex immersed; show that the equilibrium is stable, neutral or unstable, according as the specific gravity of the plate, relatively to the fluid, is greater than, equal to or less than 28. A spherical envelope contains fluid at pressure p. Determine the tension on the material. A cylindrical boiler is made with hemispherical ends; show that these ends need to have only half the thickness of the cylindrical portion, but will take the same amount of material as would be required for flat ends. u 56905. R (15) 29. A cylindrical vessel, radius 1 yard, is filled with water to a depth of 3 feet. On a level of 20 feet below the bottom of the vessel an empty cylindrical vessel stands, whose radius is 1 foot. If half the water in the upper vessel is drawn off into the lower vessel, find the diminution of the potential energy of the water. How many foot-pounds of work would it require to replace the water? (25) 30. Two quantities of a perfect gas have equal volumes (v) under pressures pi and P, respectively. They are put together and the joint volume is 2v; find the new pressure, assuming the temperature to be constant. (15) 31. Define absolute temperature; show that the product of the pressure and volume of any given mass of gas is proportional to its absolute temperature. A mass of air at 0° C. is at atmospheric pressure; its volume is quadrupled and its temperature reduced; its pressure is then found to be th of atmospheric pressure: find its temperature. (25) 32. State what is meant by the dew-point. What is meant by the tension of the vapour in the air? And how is it measured? It is known that at a temperature of 20° C. the pressure of aqueous vapour is 0.664 in. of mercury. A certain quantity of dry air has a volume of 1 cubic foot at 20° C., under a pressure of 29.2 in. of mercury. If it become saturated with aqueous vapour without change of pressure or temperature, what will be the volume of the saturated air? SUBJECT VIII. SOUND, LIGHT, (30) INSTRUCTIONS. Read the General Instructions on page 3. Stage 1. You are permitted to answer only eight questions. No candidate will be allowed to pass the examination who fails to show a competent knowledge in at least two of the sections into which the paper is divided. The examination in this subject lasts for three hours. SOUND. 1. Explain how the loudness and the pitch of a note depend on the nature of the vibrations causing the sound. (12) 2. How may the velocity of sound in air be measured? Explain generally how it is affected by wind and temperature. (12) 3. Distinguish between longitudinal and transverse waves, and give two examples of each. (12) 4. Explain what is meant by a simple harmonic vibration. Draw a curve showing the character of such a vibration by plotting the displacement against the time. LIGHT. (13) 5. What must be the height and position of a plane mirror in which a man, 6 feet tall, is just able to see himself standing upright? Draw a diagram to illustrate your answer. (12) 6. Give a geometrical construction for finding the image of a small object on the axis of a converging lens, illustrating the two cases: (a) when the image is real, (b) when the image is virtual. (12) 7. Draw the paths of a ray of light through a glass plate 2 inches thick for angles of incidence 30° and 60°, if the index of refraction is 1.5. (13) 8. Explain how you would find by experiment the centre of curvature of a concave mirror. (12) HEAT. 9. A centigrade mercury thermometer reads +1.0° when placed in melting ice and 99 5° in steam at 760 mm. If the bore of the tube is uniform, and the divisions are equal in length, what would the thermometer read at 20° C. ? (12) 10. What do you understand by the coefficient of expansion of a gas? What precautions would you take in measuring it? (13) 11. Explain how you would measure the latent heat of vaporisation of steam. (13) 12. Define the terms:-thermal capacity, water equivalent, and specific heat; and describe a simple form of calorimeter. (12) SUBJECT VIIIa. SOUND. Stage 2. You are permitted to answer only seven questions. The examination in this subject lasts for three hours. 1. Explain the term Elasticity as applied to solids. What modulus of elasticity is concerned in the propagation of sound in a rod, and how may it be determined ? (30) |