thread, and what would be its velocity relative to the lift at the instant of striking the floor? [g= 32 feet per second per second." 3. A body is projected with a velocity of 64 feet per second up a smooth inclined plane (inclined at 30 to the horizontal) in a direction making an angle of 45 with the line of greatest slope. Find the time taken by the body to return to the original level and the horizontal distance traversed. 4. Define coefficient of friction, angular velocity. A body is placed on a circular table at a distance of 3 feet from the centre. With what angular velocity may the table be rotated about a vertical axis through the centre before the body begins to slip? How would this velocity depend on the place on the earth's surface at which the experiment is performed? [Coefficient of friction between body and table = ·6.] 5. What is meant by "pressure at a point" in a fluid, “contre of pressure"? A cubical box of edge 2 feet with one pair of faces horizontal is half filled with water and half with oil of specific gravity 8, the oil floating on the water. Calculate the total pressure on the bottom and on one of the sides of the box; and the position of the centre of pressure on the side. B. 6. What do you understand by "total reflexion"? Describe a method of determining the refractive index of any substance by total reflexion. Determine the critical angle at the surface of separation of glass and water. μ glass = 1.55 Mwater = 1·33. 7. How has the velocity of light through air been determined? Given the velocity through air under atmospheric conditions, what do you know of the velocity through the specimen of glass referred to in question 6? Does the velocity of light depend on the colour of the light? 8. What is meant by the "mechanical equivalent of heat"? A body weighing 10 lbs. starts from rest to slide down a rough inclined plane. When it has descended a vertical distance of 50 feet its velocity along the plane is 20 feet per second. Find the quantity of heat generated by friction. One water pound degree Fahrenheit 772 foot-pounds. = 9. Define the coefficient of linear, superficial, and cubical expansion, and find the relation between them. Discuss the effect of a rise of temperature on (a) the cross-sectional area of a barometer tube, (b) the height of a barometer. 10. Describe and explain the changes in the appearance of the image of an object which is gradually moved from the surface of a concave mirror along the axis when viewed from a point near the axis at a considerable distance from the mirror. C. 11. Describe how you would experimentally study the variation of magnetic force along the line of the axis of a bar magnet. From your observations what would you learn of the law of force between two point poles ? 12. Define potential, capacity, condenser. Describe an experiment showing how the capacity of a condenser depends on (a) the distance apart of the plates, (b) the medium between the plates. 13. Define resistance, specific resistance. A battery of E.M.F. = 2 volts has its terminals connected by a wire of resistance 3 ohms. It is found that a current of 4 ampère flows round the circuit. Find the resistance of the battery, and the difference of potential between its terminals when the current is flowing. circuit. Find the resistance of the battery, and the difference of potential between its terminals when the current is flowing. 14. Explain the terms electrolysis, electrolyte, ion, electro-chemical equivalent. State the laws of electrolysis. An electric current is passed through a solution of copper sulphate and a tangent galvanometer in series. The galvanometer coil consists of 10 turns of wire of 20 centimetres radius. The needle is suspended at its centre. How long must the current be passed to get a deposit of copper of average thickness millimetres on a kathode 100 sq. cm. in area when the deflexion of the galvanometer needle is 30° ? Electro-chemical equivalent of copper = 00032 gram per Coulomb. Horizontal magnetic intensity = 18 absolute units. 15. Give a general account of the phenomena of electro-magnetic induction. Describe and explain the action of an induction coil. CIVIL SERVICE COMMISSION. MILITARY ENTRANCE EXAMINATION. November and December 1910. MATHEMATICS I. PAPER 1. (Three hours.) For full credit your work must be immediately intelligible, and your results given only to the degree of accuracy that is asked for or is justified by the data. The slide rule may be used whenever it allows of sufficient accuracy, and in each case a note of its use should be made. 1. A small tank has a square base ABCD measuring 30 cm. each way, and vertical sides AE, BF, &c., 18 cm. high, and contains water to a depth of 16 cm. (Fig. 1, see opposite page). How many c.cm. of water are there in the tank? The tank is gradually tilted about the edge BC and the water allowed to run out. What volume of water remains when the corner A is in the surface of the water? Draw the tank half-size, and measure with your protractor the angle which the edge AB then makes with the horizontal. Give an expression for the volume of the water remaining, as the tank is gradually tilted, (1) in terms of the length of AE under water, for cases in which the corner A is covered, and (2) in terms of the length of BA under water, for cases in which A is above the surface. Find, by drawing, the inclination of the edge AB to the horizontal when a quarter of the water has run away, and when half the water has run away. 2. A piece of cardboard is pinned to the table at the point 0 and is free to rotate about the pin (Fig. 3, see opposite page). A force P of 1 kilogram is applied at the point A in the direction AB. Another force Q is applied at C in the direction CD. Prick the figure through into your book and find the magnitude of the force Q which will hold the cardboard still, and the magnitude and direction of the force exerted by the pin. 3. AOB is the diameter of a circle whose centre is at 0. At C in the circumference a tangent CE is drawn. OE parallel to AC meets this tangent in E. Prove that EB touches the circle, and find an expression for the distance EB, in terms of "r" the radius of the circle, and "e" the angle COA. |