III. (a.) If there be six turns of a screw in 1 inch, and if the power arm be 1 foot in length; find what resistance will be balanced by a power of 20 lbs., neglecting fraction. (b.) A crane is worked by means of a winch 15 inches long, which turns a pinion of 6 teeth. These work in a wheel of 80 teeth and on the axle of the latter is the cylinder 10 inches in diameter for receiving the rope. What weight can a man raise with such a crane, supposing he can exert a force of 100 lbs. at the handle ? IV. A weight of 400 lbs. rests on a plane inclined to the horizon at an angle of 15°, the limiting angle of resistance being 34° 40′ Determine the pressure which will just not pull the body down; first, when its direction is inclined upwards from the horizon at 10°; next, when its line of action is parallel to the plane; and lastly, its magnitude and direction when the least possible. V. A body is projected upwards from the top of a tower 200 feet in height with a velocity of 40 feet per second, at the same time that another body is projected upwards from the bottom of the tower with a velocity of 90 feet per second. Where will they meet? VI. A body weighs W lbs., and is pulled up an inclined plane by a pressure P that acts parallel to the plane; show that the sin (a+w).) g. where a is the COS w inclination of the plane and ∞ the limiting angle of resistance. VII. A=2, B=3, are two perfectly elastic bodies-A, moving with a velocity of 20 feet per second, impinges directly on B. moving in the opposite direction with a velocity of 12 feet per second; find their directions and velocities after impact. VIII. Explain the action of centrifugal force. On a railway of 5' 6" gauge, a curve of half a mile radius is to be laid for a speed of 40 miles per hour. Find the amount of superelevation that should be given to the outer rail in order to counteract centrifugal force. IX. A train proceeding at 30 miles an hour on a level lineaverage resistances being 10 lbs. per ton-is supplied with brake power equivalent to 20 lbs. per ton. Steam being shut off at half a mile from a station find at what point the brakes must be applied in order that the train may be brought to a stand opposite the station. Find also the time occupied in running the half mile. SATURDAY, 19TH FEB., 2 TO 5 P.M. I. Prove that in a heavy homogeneous liquid at rest, the pressure at any depth varies as the depth below the surface-Also that the common surface of two liquids that do not mix is a horizontal plane. II. An isosceles triangle has its vertex in the surface of a fluid, and its base horizontal: find the total pressure and the centre of pressure. III. The lighter of two fluids, whose specific gravities are as 2: 3, rests on the heavier to a depth of 4 inches. A square is immersed in a vertical position with its side in the upper surface; determine the sides of the square in order that the pressures on the portions in the two fluids may be equal. IV. When a vessel is filled by means of equal volumes of two fluids the specific gravity of the compound is double what it would be if the vessel were filled by means of equal weights of the fluids. Compare the specific gravities of the fluids. V. (a) Describe the hydrostatic balance, and show how to compare the specific gravities of a solid and a liquid when the liquid is the heavier of the two: (b) A ring consists of gold, a diamond, and two rubies, and weighs 44 grains in air, and 383 grains in water. When one ruby is taken out it weighs 2 grains less in water. Find the weight of the diamond, the specific gravity of gold being 164, of diamond 3, and of ruby 3. VI. Describe fully the hydrostatic press and show how the relation of P to W can be obtained. Describe also the action of the common fire engine. VII. Shew how to graduate a thermometer and a barometer. If the sum of the two readings of Fahrenheit's and the centi grade thermometers for the same temperature be zero; find the reading of each thermometer. VIII. If a glass tube, 36 inches long, closed at the top be gunk perpendicularly into water till its lower or open end be 30 inches below the surface of the water, how high will the water rise within the tube, the height of the barometer being 29 inches, and the specific gravity of mercury 13.568. IX. Two volumes and V' of different gases at pressures p, p', and temperature t, are mixed together. The volume of the mixture being X and its temperature t' determine the pressure. X. Explain the principles involved in levelling by the barometer, and by the boiling point of water. APPENDIX. MATRICULATION EXAMINATION. I. TUESDAY, 21ST DEC., 10 A.M. TO 1 P.M. URIYA: GRAMMAR, &c. REV. K. M. BANERJEA, LL.D. ଖ୍ରୀଷ୍ଟୀୟ ୩୭୬ ସାଲରେ ଆଶିୟା। ମହାଦ୍ବୀପର ମଧ୍ୟସ୍ଥଲଠାରୁ ଆଗର ହନ୍ ନାମକ 'ଅଣ ଅସଭ୍ୟ ଏକ ଜାଈ ଋଷି ଦେଶସ୍ଥ ବଲ୍ଗା ନଦୀ ପାର ହୋଇ, ଦାନୁଦ ନଦୀର ଖର ପର୍ଯ୍ୟନ୍ତେ ବ୍ୟାପ୍ତ ହୋଇଲେ । ଭହିରେ ଋଷିଗୋପୀୟ ଲେକମାନେ ସେମାନଙ୍କରଠାରୁ ରକ୍ଷା ପାଇବା ନିମନ୍ତେ, ସୈମୀୟ ଗ୍ରଜ୍ୟର ଅଭ୍ୟନ୍ତରେ 'ଅର୍ଥାତ୍ ଦାନ୍ତ୍ରିକ ନଦୀର ଦକ୍ଷିଣ ଘରରେ ବସ କରବାର ଅନୁମତ ମାଗନ୍ତେ, ତତ୍କାଳିକ ସେମୀୟ ଗଜାସ୍ତ୍ର ଗୁଜ ସେମାନଙ୍କୁ କହିଲେ, ‘* ଘୁମ୍ଭମାନଙ୍କର ବଲବାନ ପୁଷମାନେ ଯେବେ ସେମୀମାନଙ୍କର ପକ୍ଷରେ ସୈନ୍ୟରୂତ୍ୱ ସ୍ଵୀକାର କରନ୍ତି ତେବେ ଆମ୍ଭେ "ଅନୁମତ ଦେବ ।” ଏହି ନିୟମାନୁସାରେ ସେମାନେ ପ୍ରେମୀ ସଜ୍ୟରେ ପ୍ରବେଶ କରିଲେ ପ୍ରମାଣ, ତଥାପି ସ୍ଵାଧୀନ ରହିଲେ । ପଶ୍ଚାତ୍ ପ୍ରେମୀମାନଙ୍କର ଅଶ୍ୟାମାନ ଓ ବଣ୍ଟାସଘାତ୍ମକତା ପ୍ରଯୁକ୍ତ, ସେମାନଙ୍କର ଓ ଗୋପୀମାନଙ୍କର ମଧ୍ୟରେ ପରଞ୍ଚିର ଦୁର୍ବୃଦ୍ଧି ଜନ୍ମବାର୍ ଅର୍କାଦସର ଗଜମନ୍ତ୍ରୀ ଅପଣା କର୍ପୂର ଗଜ୍ୟରକ୍ଷା କରବାର 'ଅଣ୍ଡ୍ପ୍ରାୟରେ, ଗୋଥାମାନଙ୍କୁ ଇଭାଲି ଦେଶରେ ଯାଏ। କରିବାର ପ୍ରବୃତ୍ୟୁ ଦେଲେ । (a) How would the first three words giving the date in the above extract be written in an Uriya manuscript letter or document ? |