sin B sin a. 1. Describe an arrangement by which the parallelogram of foroesi 15 may be experimentally verified. show how to find. graphically or otherwise, the rosaltant of forces Acting on a rigid body nt one point, and apply sont method to find the reanltant of forces. 1 in an eusterly direction, ✓7 in a north-easterly direction and I to the north. 2. State and prove Lami's theorein. 20 Two forror Pand Q art at a point along two lines which are inclined at an angle a and F is their resnltant: two other foroar. Pand Q', arting along the same lines have a rosnltant F. If B is the angle between the lines of action of F and F prove that P.Q-P.Q FF. 3. Find the conditions of equilibrium of a system of forces acting in one plane. A nniform rod of weight. Wind length 2n is reeting with its middle 20 point supported by the highest point of a perfect'y'rongh Aphere of radius Weights P and Qure tachod to its extremities and it is left to find ita equilibrinm nosition Prove that in this position the circular measure of the inclination of tbe rod to the horizontal is a (P-Q) r (P+Q+W) 4. A rhombns ABCD is formed of fonr eqnai weightless rod 8 freely 15 jointed at their extremities. The angular points B D Are joined by string. and the system is strained by means of + second string connecting points in AD BC and perpendicnlar in direction to these rides. 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. ABOD a binged framework formed with five light rods AB, BC, 15 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 diagranı may be drawn giving the stresses in the various rods and at the supports, and explain the principles involved. 6. A bridge is formed of a uniform rod of length 2a resting hori. 15 .zontally on snpports 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 circamstances under which it arises. 7. If I and t be the units of length and time when f 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 onit 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. 19. Wlíat is mešnt by vis viva and work. Assnming the principle of 15 conservation of energy, find the height through which a body falls'uðdei gravity in a given time. 10" The diameter of the circular piston of a steam-engine is 60'inches, 15 it makes 11 strokes per minute, the length of each stroke is 8 feet. the mean pressure per square inch on the piston is 15 lbs., the modulas ) 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 15 assuming the cone to be circular, a : The figures in the margin indicate full marks. 1. Define a fluid: and state its fundamental property. Indicate how 25 fluid presgnre is measured : and give a measure of the flạid pressure at any point of an immersed surface. 2. "Prove that pressure at a point is eqnal'in all directiong. 20 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 one 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 namerical values and work out, the result in that particular case. 4. Prove that the pressure at any point of a flaid at rest is expressed 30 by the formula p=gpz : state the system of units involved. 30. -Find the pressare in pounds weight *t'ai deptiiibt50 feet it wáter_(1).E neglecting, (2) taking account of the atmospheric pressure. 5. Prove thathe depth of the centre of pressure on aatettabġntar 230 area immersed in Huid with oné side in the surface-is-two-thirds the will depth of the opposite side of the rectangle. Prove that in the rectangle is lowered in'the fluid, the centre of près... sure approaches and ultimately coincides with the centre of gravity of ein he rectangle, 6. Find the resoltant pressure on a surface exposed to faid pressure. ,30 A closed hemispherical vessel is just filled with fluid and is held with its plane base vertical : compare the pressgres on the lower and upper halves of the carved surface. 7. Find the conditions for equilibrium of a floating body. A cylinder floats, with its axis vertical, partly immerged in two liquids the densities. of the upper and lower liquids being respectively pand 2p, 8p and the density of the cylinder ; find the position of equilibriam 'fo 4 the cylinder, its length being twice the depth of the npper fluid. 8. Define the metacentre, and show how the stability of a body de 20pends on the position of the metacentre. 9. State Boyle's law, and describe an arrangement whereby the law.po may be verified: :: A hollow cylinder open at the top is inverted and partly immersed in () water; find the beight of the surface of tue water inside the cylinder. 10. Explain the meaning of the terms intrinsic weight, density, 35 specifio gravity. If the specific gravities and volumes of the constitaents of a mixtare 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 flaids, the densities of inte 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 2014 determination of specific gravities. .. 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 yọn anderstand by the terms: step-Sault, overthrust, dyke, dome, unconformity ? 25 2. A coal-seam, which crops ont in level country, is ten feet thick, 25.and has a strike of N 20° E to $ 20° W and a dip of 450 to E 20° 8 : what would be the distance from the outcrop to the nearest point at: whichila 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. " witat would be the length of the core derived from it in this vertical boring? Illustrate your answer by means of a diagram. .. water. 3. Devoribe briefy the differont forms of laterito. Are any of them 20 of boonomio #100 %. If sö, for what purpovos aro they omplayed ?-,,,152 4. Boomerate the chief subdivisions of the lower Gondwanan of Bengal. How would you distinguish between Talchir sandstono and Burakar ':*: sandstone ! 6. State the class to which each of the following fossils belongs : io * what stratigraphical systems do they occar?.. (a) Gangamopteris cyclopteroides, (n) Stegodon ganesa, (c) Physa 26 prinsepii, (d) Productus semireticulatus (e) Nummulites ramordi. 6. What is an arterian well"? Illustrate your answer by means of a 25 diagram showing the conditions favourable to the existence of artesian 7. State briefly the nature and 'most characteristic features of the 26 Deccan trap: Is the trap of economic value? If.8«, for what porpose or parpodes ? 8. What do you understand by the term erosion? In what manner. 25 may the erosive action of a river canse serious damage to towns situnted on its hanks, and how may the effects of this action be' counterarted? 9. Name' the posenttial constitüents and a few common accessory cob. stituents of the following rocks : (a) Hornblende-granite, (6) 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 Kidilerpore locks, in whii h it was decided to build the dock-walls of brick, fared with basalt, and huviug qnoins formed of large slabg": of. either granite or churriokite, from what part of India, having dne regard to economy and effisiency, wonld your propo-e: to obruin euch of the above materials, and what part of India would furnish the lime for pour mortar? 11.. Whut, are lundslins.? Indirgre, the structorul conditions ander * 25 which they are lible 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, brachypinncoid, pleochroism." 25 2. Name the two commonest species of mica occurring in granite ; :1 25 show would yon distingnish them from ova unother mod from rule 2 3. What are the chief uses of manganese ? Enumerate its most im; .; 25 portant ores. 26 the How would you distinguish between : ras red garnet and ruby, (d) oligoclase sud labradorito? 6. An iron ore is found on analysis to have tho following composi. tion : Fe 70 por cent. 0 30 3 Calculate its chemical formula and give the name of the oro. (The 26 atomic weight of iron in 56 and of oxygen 16) 7. Derorile gnite briefly. the method commonly employed for tho, 25 recovery of gold, on a commercial scale, from a free-milling ore such as that of Rolur 8. Whut in forro-manganeso ? How is it made and for wliat purpose“ 25 is it employed ? 9. Whit i- the romposition of each of the following alloys':pewlog gin metal, hrana, aluminiurn-bronze commin xolder ? 25 10. What is the chief 'ore of aiaminiam ? How is it trented for the 25 recovery of the metal ? 11. What in the affect of the presence of each of the following ele. . 25 menta in steel: sulphur, phosphorus chromium, tungsten ? 12. : , What do y.lt ww.leratanut hy the twrm “ recovery. oven in counec. tion with coke-making ?. Saime a wellknown 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 gipen yon. 2. Prepare appruximately 1} ounce of the alloy named in the accompany. ing slip. PRACTICAL PHYSICS. Examiner-A. MACDONELL, Esq., M.A. Thore of the following experiments are to be made. 1. Find the sperifio gravity of a mlid. 1.2. Dotoopinvisie the pulm of crystiil 3. Find tbo moment of invertis of a bar. |