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1. Desrriba an arrangement by which the parallelogram of forces 15 may be experimentally verified.
show how to find. graphically or otherwise, the rosnltant of forces acting on x rigid body at one point, and apply ponr method to find the resnltant of forces. 1 in an ensterly direction, ✓2 in a north-easterly direction and I to the north, 2. State and prove Lami's thenrein.
20 Two former Pand Q act at a point along two lines which are inclined at an angle a And Fis their resoltant: two other foroar. P' and Q, arting along the same lines have a resnltant F. If B is the angle between the tinor of action of Fand F prove that
P.Q' - P'.Q sin B
FF. 3. Find the conditions of equilibrium of a system of forces acting in one plane.
A nniform rod of weight. W und length 2a is reeting with its middle 20 point supported by the highest point of a perfect'y'rongh Ruhera of rudius
Weights P and Quro itached to its extremities and it is left to find ita equilibrinm nosition Propa thar in this position the circular measure of the inclination of the rod to the horizontal is
g (P+Q+W) 4. A rhombns ABCD is formed of fonr eqnai weightless rod 8. freely 15 jointed at their extremities. The angnlar pointa B D are joined by a string, and the system is stisained by means of a second string connecting points in AD BC and perpendicnlar in direction to these rides.. If T dennte the tension in the latter atring, 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, 15 CD, AC, and AD, rests with AD horizontal on two supports at A and D and carries weights at the hinges B and O. Show how a stress diagram 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 maxi. mum value, indicating the cirdamstandes 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, fipd, the units of acceleration and velocity when l' and t are the units of length and time.
If the acceleration dae 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 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 mëänt by vis viva and work. Assuming the principle of 15 conservation of energy, find the height through which a body falls nåder gravity in a given time.
10" The diameter of the cironlar piston of a steam-engine is 60'inchès, 15 it makes 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 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,
The figures in the margin indicate full marks. 1. Define a fluid: and state its fundamental property. Indicate how 25 Huid pressure is measured : and give a measure of the fạid pressure at any point of an immersed surface. 2. Prove that pressure at a point is eqnal'in all directions.
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 abont 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 nomerical values and work, apt, the result in that particular
4. Prove that the pressure at any pbing of a fluid at rest is expressed 30 by the formula p=gpz : state the system of units involved.
Find the pressure in pounds weight *tiai depthi bf-50 feet iti water-(1) .E neglecting, (2) taking account of the atmospheric pressure. *1.7" : Y
5. Provide that the depth of the centre offres àre on a'tëčlangnyar #30 area immersed in Huid with one side in the surface is two-thirds the woll depth of the opposite side of the rectangle.
Prove that is the rectangle is lowered in'the fluid, the centre of près.. sure approaches and ultimately coincides with the centre ofigravity of eti" he rectangle. 6. Find the resoltant pressure oq a surface exposed to figid pressure...30
A closed hemispherical vessel is just filled with fluid and is held with its plane base vertical: compare the presspres on the lower and upper balves 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 thie upper and lower liquids being respectively pand 2pac
8p and the density of the cylinder- ; find the position of equilibrian '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.30
Å hollow cylinder open at the top is inverted and partly immersed in. (5.) water; find the beight 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 mixtare be given, find the specifio gravity of the mixtære, noting any assumption made ia the course of the proof.
A mixture is formed of eqnal volumes of flaids, the densities of 107 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.
... :. .:
Examiner H. H. HAYDEN, Esq., B.A., B.E., ÉG.S.
The figures in the margin indicate full marks.
(Not more than EIGHT questions to be attempted.).
1. What do you anderstand by the terms: step-Sault, overthrust, dyke, dome, unconformity ?
25 2. A coal-seam, which crops out in level country, is ten feet thick, 25.and has a strike of N 20° E to 3 20° W and a dip of 450 tö E 200 S: what would be the distance from the oatcrop to the nearest point at which la vertical boring could be put down to strike the coal-seum at a depth of 500 feet below the surface, and what would be the compass, bearing of that point from the outcrop ? If the tliickness 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.
3. Desoribo, briefly tho diføront forms of laterito. Ano any of them 20 of economio vA100 ?If so, for what purpoibok aro they omployed 2.53.19
4. Boomerate the chief sabdivisions of the lower Gondwana. of Bengal. How., would you distinguish betwoon Tolchir sandstone and Burakar sandstone !
6. . State the class to which cach of the following fossils belongs : io * what stratigraphical systems do thoy occor ?...
(a) Gangamopteris cyclopteroides, (n) Stegodon ganesa, (e) Phydd 26 prinsepii, (d) Productus semiroticulatus; (e) Nummulites ramordi.
6. What is an arterian well ? Illustrate your answer by, moana of A 25 diagram showing the conditions favourable to the existence of artesian water.
7. State briefly the nature and most characteristio features of the 26 Deccan trap: Is the trap of economic value? If.80, for what porpose or porposes ?
8. What do you understand by the term erosion? In what manner 25 may the erosive action of a river cango serious damage to towns situnted on its hanka, and how may the effects of this action be'counterarted?
9. Name' the essential sonstitüênts and a few common accessory constituents of the following rocks :
(n) "Hornblende-granite, (5) mica-apatite-peridotite, (c) augite. norite 25 (d) eläolite-syenite, (e) charnockite.
10. If you were called upon to undertake the building of an extension 25 of the Kidilerpore locks, in which it was decided to haili the dock-walls of brick, fared with basalt, and huviug qnoins formed of large slabo : of. either granite or churniorkite, from what part of India, having dne regard to economy and effisiency, wonld you propo-e to obruin esch of the above materials, and what part of India would furnish the lime for pour mortar ?
11. What are lundsling.? Indirate the structorul conditions änder: 25 which they are li- ble to occur and the nature of the precautions to be adopted for their prévenrion. 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 ;:i 25 whow would yon distingnish them from ove another and from unde?
3. What are the chief uses of manganesp ? Enumerate its most im; ; 25 portant ores.
the How would you diatingaish between
ras red garnet and ruby,
26 .o. If you wore given a sample of sand composed of grains of aaloito, . magnetitr, quartz, opal wod garnet, how would you isolato each of tbono constit dents ?
25 6. An iron ore is found on analysis to have the following composi. Fe
70 por cont. 0
Calrulate its chemical formula and give the name of the oro. (The 26 atomic weight of iron in 56 and of oxygen 16)
7. · Dercribe quite briefls the method commonly employed for the 25 recovery of gold, on u commercial scale, from a free-milling ore such as that of Kolur
8. Whut in forro-mauganese ? How is it made and for wliat parpose 25 is it employed ? 9. What is the composition of each of the following alloys':pewlor gon metal, hrasx, aluminiu.n-bronze, ícou main xolder ?
25 10. What is the chief'oro of alaminiam ? How is it trented for the 25 recovery of the metal ?
11. What in the affect of the prerelice of each of the following ole. . 25 ments in steel: sulphur, phosphorus chromium. Tungsten ?
12., What do you on lerntanit by the throu fecovery, oven in counec. tion with coke-muking ? Swine a well-known type of recovery opon, and Augmerate the useful products obtained from it.
Examiner-H. H. HAYDEN, Esq., B.A., B.E., K.G.S.
1. Determine the percentage of coke in the simple of coal giren yon.
2. Prepare appruximately 1} ounce of the alloy named in the accompany. ing slip.
Examiner-A. MACDONELL, Esq., M.A.
Thrre of the following experiments are to be made.
t. Find the sperifio gravity of a onlid. 1.2. Detaip visie the puglo of u crystiil
3. Find tbe moment of ivertis of a bar.