1. Describe an arrangement by which the parallelogram of forces, 15 may be experimentally verified. Show how to find. graphically or otherwise, the resultant of forces acting on a rigid body at one point, and apply your method to find the resultant of forces 1 in an easterly direction, 2 in a north-easterly direction and 1 to the north. 2. State and prove Lami's theorem. Two forces P and Q act at a point along two lines which are inclined at an angle a and Fis their resultant: two other forces, P′ and Qʻ, acting along the same lines have a resultant F". If B is the angle between the lines of action of F and F prove that 20 3. Find the conditions of equilibrium of a system of forces acting in one plane. A uniform rod of weight Wand length 2a is resting with its middle 20point supported by the highest point of a perfectly rough sphere of radius Weights P and Q ure "ttached to its extremities and it is left to find its equilibrium position Prove that in this position the circular measure T. of the inclination of the rod to the horizontal is 4. A rhombus ABCD is formed of four eqnai weightless rod s freely 15 jointed at their extremities. The angular points B D are joined by a string, and the system is strained by means of » second string connecting points in AD BC and perpendicular in direction to these sides. If T denote the tension in the latter string, and a the angle between the sides AB, BC, show that the tension in BD is 5. ABCD a hinged framework formed with five light rods AB, BC, CD, AC, and AD, rests with AD horizontal on two supports at A and D and carries weights at the hinges B and C. Show how a stress diagram may be drawn giving the stresses in the various rods and at the supports, and explain the principles involved. 15 6. A bridge is formed of a uniform rod of length 2a resting hori- 15 zontally on supports at a distance e from either end. Find the bending moment at any point of the rod as a man walks across; also its maximum value, indicating the circumstances under which it arises. 7. If land t be the units of length and time when ƒ and v are the 20 units of acceleration and velocity, find, the units of acceleration and velocity when l' and t' are the units of length and time. If the acceleration due to gravity per second be taken as the unit of acceleration, and the velocity generated in one minute as the unit of velocity, find the unit of length. 8. Assuming that the external impressed forces are equivalent to the 20 effective forces, in the case of a particle moving in a vertical circle under gravity, write down the equations of motion and find the velocity at any point of the circle. A particle is projected horizontally with velocity v from the 20 highest point of a smooth vertical circle: find when it will leave the circle. 9. What is meant by vis viva and work. Assuming the principle of 15 conservation of energy, find the height through which a body falls under gravity in a given time. ༢." 10 The diameter of the circular piston of a steam-engine is 60 inches, 15 it makes 1:1 strokes per minute, the length of each stroke is 8 feet. the mean pressure per square inch on the piston is 15 lbs., the modulus > of the steam-engine being 65. Determine the number of cnbic feet of water it will raise per hour from a well the depth of which is 300 ft." 11. A particle is moving in a straight line under the action of a force 15 varying as the distance from a point in that line: find the time of an oscillation and the velocity at any point.' 12. Describe the conical pendulum, and find the time of a revolution assuming the cone to be circular, 15 HYDROSTATICS. Examiner C. LITTLE, Esq., M.A. The figures in the margin indicate full marks. 1. Define a fluid: and state its fundamental property. Indicate how fluid pressure is measured: and give a measure of the fluid pressure at any point of an immersed surface. one 20 2. Prove that pressure at a point is equal in all directions. 3. A safety valve consists of a heavy rectangular lid which is hori- 30 zontal when it closes the aperture beneath it, and is moveable about or side. The aperture being a square which is coincident with the fixed side of the lid, find the maximum pressure marked by the valve. Assume numerical values and work out, the result in that particular case. 4. Prove that the pressure at any point of a fluid at rest is expressed by the formula p=gpz: state the system of units involved. *Find the pressure in pounds weight at a depth of 50 feet in water (1) E neglecting, (2) taking account of the atmospheric pressure. Bre 5. Prove that the depth of the centre of pressure on a rectangular 230 area immersed in fluid with one side in the surface is two-thirds the li depth of the opposite side of the rectangle. Prove that as the rectangle is lowered in the fluid, the centre of pres. sure approaches and ultimately coincides with the centre of gravity of he rectangle. 6. Find the resultant pressure on a surface exposed to fluid pressure.. 30 A closed hemispherical vessel is just filled with fluid and is held with its plane base vertical: compare the pressures on the lower and upper halves of the curved surface. 7. Find the conditions for equilibrium of a floating body. A cylinder floats, with its axis vertical, partly immersed in two liquids the densities of the upper and lower liquids being respectively pand 2p, and the density of the cylinder ; find the position of equilibriam fo 3p 4 the cylinder, its length being twice the depth of the upper fluid. 8. Define the metacentre, and show how the stability of a body de-20 pends on the position of the metacentre. 9. State Boyle's law, and describe an arrangement whereby the law 30 may be verified. A hollow cylinder open at the top is inverted and partly immersed in (E) water; find the height of the surface of the water inside the cylinder. 10. Explain the meaning of the terms intrinsic weight, density, 35 specific gravity. If the specific gravities and volumes of the constituents of a mixture be given, find the specific gravity of the mixture, noting any assumption made in the course of the proof. A mixture is formed of equal volumes of n fluids, the densities of 2207 which are in the ratio of the numbers 1, 2, 3.....n; find the density of the mixture. 11. Describe the common hydrometer; and find its formula for the 20 determination of specific gravities. GEOLOGY. Examiner H. H. HAYDEN, ESQ., B.A., B.E., F.G.S. The figures in the margin indicate full marks. (Not more than EIGHT questions to be attempted). 1. What do you understand by the terms: step-fault, overthrust, dyke, dome, unconformity? 25 .S 2. A coal-seam, which crops out in level country, is ten feet thick, 25and has a strike of N 20° E to S 20° W and a dip of 45° to E 20° S: what would be the distance from the outcrop to the nearest point at which a vertical boring could be put down to strike the coal-seam at a depth of 500 feet below the surface, and what would be the compass-bearing of that point from the outcrop? If the thickness of the seam is constant. what would be the length of the core derived from it it in this vertical boring? Illustrate your answer by means of a diagram. 3. Describe briefly the different forms of laterite. Are any of them 25 of economic value? If so, for what purposes are they employed? Suicos 4. Enumerate the chief subdivisions of the lower Gondwanas of Bengal. How would you distinguish between Talchir sandstone and Burakar sandstone? 5. State the class to which each of the following fossils belongs : in what stratigraphical systems do they occur ? (a) Gangamopteris cyclopteroides, (b) Stegodon ganesa, (c) Physa 26 prinsepii, (d) Productus semireticulatus, (e) Nummulites ramondi. 6. What is an artesian well? Illustrate your answer by means of a 25 diagram showing the conditions favourable to the existence of artesian Water. 7. State briefly the nature and most characteristic features of the 25 Deccan trap. Is the trap of economic value? If so, for what purpose or purposes? 8. What do you understand by the term erosion? In what manner 25 may the erosive action of a river cause serious damage to towns situated on its banks, and how may the effects of this action be counteracted? 9. Name the essential constituents and a few common accessory constituents of the following rocks :— (a) Hornblende-granite, (5) mica-apatite-peridotite, (c) augite- norite 25 (d) elæolite-syenite, (e) charnockite. 10. If you were called upon to undertake the building of an extension 25 of the Kidderpore Docks, in which it was decided to build the dock-walls of brick, faced with basalt, and having quoins formed of large slabs of either granite or charnockite, from what part of India, having dne regard to economy and efficiency, would you propose to obtain each of the above materials, and what part of India would furnish the lime for your mortar? 11. What are landslips? Indicate the structural conditions under 25which they are liable to occur and the nature of the precautions to be -adopted for their prevention. 12. Define the following terms: Conglomerate, schist, grit, oolite, calcareous tufa, kunkur, breccia. 25 MINERALOGY AND METALLURGY. Examiner H. H. HAYDEN, Esq., B.A., B.E., F.G.S. The figures in the margin indicate full marks. (Not more than EIGHT questions to be attempted). 1. Define the terms : hemihedral, pseudomorph, clinodome, brachypinacoid, pleochroism. 25 2. Name the two commonest species of mica occurring in granite ;125 how would yon distinguish them from one another and from tale ?. 3. What are the chief uses of manganese ? Enumerate its most im 25 aportant ores. 4. How would you distinguish between (a) red garnet and ruby, (b) sapphire and amethyst, (d) oligoclase and labradorite? 5. If you were given a sample of sand composed of graina of calcite, magnetite, quartz, opal and garnet, how would you isolate each of these constituents ? 6. An iron ore is found on analysis to have the following composi. tion : Fe 70 per cent. 100 25 Total Calculate its chemical formula and give the name of the ore. (The 25 atomic weight of iron is 56 and of oxygen 16) 7. Describe quite briefly the method commonly employed for the 25 recovery of gold, on » commercial scale, from a free-milling ore such as that of Kolar 8. What is ferro-manganese ? How is it made and for what purpose · 25 is it employed ? 9. What is the composition of each of the following alloys : pewter gun metal, brass, aluminiun-bronze common solder? 25 10. What is the chief ore of ulaminiam ? How is it treated for the $25 recovery of the metal ? 11. What is the effect of the presence of each of the following ele.. 25 ments in steel: sulphur, phosphorus chromium, tungsten ? in counec. 12. What do you understand by the term Recovery oven tion with coke-making ? Same a well-known type of recovery oven, and enumerate the useful products obtained from it. PRACTICAL METALLURGY. Examiner H. H. HAYDEN, Esq., B.A., B.E., F.G.S. 1. Determine the percentage of coke in the sample of coal given you. 2. Prepare approximately 1 ounce of the alloy named in the accompanying slip. |