The dividend is 1857 added to the product of 902341 by 978-882491355. 2. Reducing both terms to oz. we have 5. (1) Here the divisor is 1000 times greater and the dividend 10000 times smaller, therefore the result will be 1000000 times smaller than 9027, which is 009027. (2) Similar reasoning gets 9-027 in this case. =(1·04)-1=X.124864; then £1397.5625 ×·124864 = £174.50416-£174 10s. 1d. and £3441 13s. 4d.-(£154 17s. 6d. +£3 15s. 10d.) = £3283, the sum to be divided in the second and 49 99:: 3283: £663 12s. the daughter's share, LONDON UNIVERSITY, 1. Define Velocity, Acceleration, Momentum, Force. A particle moves from rest with a uniformly increasing velocity: show that the whole space described is proportional to the square of the velocity. 2. What is the resultant of a system of forces? Is a system of forces in one plane always equivalent to a single force? If not, what exceptions occur? 3. The height of an inclined plane is threefifths of its length; a body is projected up the plane from the bottom with a velocity of 50 ft. per second, and slides down again: find the distance attained, and the time before the body arrives at the starting point. 4. Show that if a body be in equilibrium under the action of three forces they all meet in a point, or are parallel. 5. Explain how a kite is supported in equilibrium. 6. A heavy uniform beam, 10 ft. long, whose mass is 10 lbs., is supported at a point 4 feet from one end; at this end a mass of 6 lbs. is placed : find the mass required to balance the beam. 7. Two weights of 14 and 18 oz. are suspended by a fine thread which passes over a smooth pulley at a height of 30 ft. above the weights. If the system be left free to move, find how far the heavier weight will descend in the first three seconds of its motion. Find the tension of the string. 8. What is the resultant pressure exerted by a fluid on a body immersed in it? If the specific gravity of iron be 7.6, what will be the apparent weight of 1 cwt. of iron when weighed in water, and how many pounds of wood of sp. gr. 06 will be required to be attached to the iron so as just to float it? 9. What is the object of a barometer? Explain the construction of some good form of instrument. 10. Explain the fundamental difference between the common hydrometer and that of Nicholson. A Nicholson's hydrometer weighs 8 oz., the addition of 2 oz. to the upper pan causes it to be sunk in one liquid to the marked point, while 5 oz. are required to produce the like result in another liquid. Compare the specific gravities of the liquids. 11. In Nicholson's hydrometer, if the specific gravity of the weights is 8, what weight must be placed in the lower pan to produce the same effect as 2 oz. in the upper pan? 12. Describe a simple method of verifying Boyles' law. (a) The height of the top of a uniform barometer tube is 33 inches above the mercury in the tank; on account of air in the tube, the barometer registers 286 inches of mercury when the atmospheric pressure is equivalent to 29 inches of mercury. What will be the true height of the barometer when the height registered is 29.93 inches ? 13. Define the specific heat and the latent heat of fusion of a substance. (a) The specific heat of iron is 0.113: how many lbs. of iron at 250° Centigrade must be introduced into an ice calorimeter in order to produce 2 lbs. of water? 14. State the laws of evaporation. Under what circumstances will a liquid evaporate, and how must the conditions be modified in order that it may boil. What is the dew-point? 15. Describe the action of a concave lens on a pencil of light diverging from a point on the axes of the lens, and hence explain the use of concave spectacles to short-sighted persons. 16. What is the limiting angle of refraction of a medium? Light proceeds from a point under water. Make a careful drawing, showing the paths of the several rays which reach the surface of the water; explain fully what happens to each at the surface. ANSWERS. 1. Velocity is the rate at which a body moves, and is measured by the space described divided by the time of description. Acceleration is the rate at which velocity increases, and is measured by the increase of velocity divided by the time of increase. the forces, A and B, not to be parallel; then A and B meet in a point, for otherwise they would not have for resultant a single force; the force C must pass through the same point, for otherwise it would not be in equilibrium with the resultant of A and B. Hence A, B, and C meet in a point. Now, suppose A and B to be parallel; then the resultant of A and B is parallel to them, and C must be in equilibrium with this resultant, and therefore parallel to A and B. 5. A kite is kept in equilibrium by the action of three forces: firstly, its own weight, which acts vertically downwards through its centre of gravity; secondly, the tension of the string; thirdly, the pressure of the wind on the kite, which is normal to its surface and acts through its centre of figure, and which varies in magnitude according to the angle the kite makes with the direction of the wind. When the kite is flying it takes such a position that the resultant of the pressure of the wind and the tension of the string acts vertically upwards through its centre of gravity. 6. The weight of the beam acts at its centre, which is one foot from the point of support. Hence, if x be the required mass, we have— 6 × 4 10 × 1 + x × 6 = Fortin's barometer consists of a glass tube sealed at the upper end, which dips into a cistern of mercury. The cistern and about thirty inches of the tube contain mercury, the space between the mercury and the upper end of the tube is a vacuum. The cistern is formed of a glass cylinder, through which the level of the mercury may be seen. The bottom of the cistern is made of a bag of flexible leather, against which a screw works. At the top of the interior of the cistern is a small piece of ivory, the point of which coincides with the zero of the scale for reading the height of the barometer. By means of the screw the level of the mercury in the cistern can be raised or lowered t.ll its surface just touches the ivory point. The upper part of the scale is graduated so as to show the height of the mercurial column above the level of the mercury in the cistern. A vernier slides on the scale, and in taking a reading the index attached to the vernier is brought level with the top of the convex surface of the mercury. The whole instrument is enclosed in a brass tube, which swings on pivots in such a manner as to allow the tube always to hang truly vertical. A thermometer is attached to the instrument, which is read at the same time as the barometer, for the purpose of applying the correction for the temperature of the mercurial column. 10. In the common hydrometer, the weight of the instrument is invariable and the bulk of the liquid displaced is measured by the depth to which the stem sinks in the liquid. In Nicholson's bydrometer, the bulk of the liquid displaced by the instrument is invariable, and the weight of liquid displaced is determined by that of the instrument and added weights. (The specific gravity of the first liquid is to that of the second liquid as 8 + 2 is to 85, or as 10 to 13.) 12. A long glass U tube is taken, one leg of which is of some length, and open at the end, the other leg closed, and but a few inches long. The shorter leg is graduated to show equal capacities; the longer leg is graduated to show the height above the zero point, which is at the same level in both legs. The tube is fixed vertically and a small quantity of mercury poured into it, so that the mercury may stand at the zero point in both legs. The air in the shorter leg is now under the atmospheric pressure at the time of the experiment. Mercury is next poured into the longer leg of the tube till the bulk of the air in the shorter tube is reduced to one half. The difference of the heights of the mercury in the two legs is then read off. If this is found to be equal to the height of the barometer at the time of the experiment, the air in the short leg of the tube must be subjected to double the atmospheric = Therefore the true height of the barometer 29.93+0.57 30 5 inches. 13. The specific heat of a substance is the ratio of the quantity of heat required to raise the temperature of a given weight of the substance one degree, to the quantity of heat required to raise the temperature of the same weight of water one degree. The latent heat of fusion of a substance is the quantity of heat which disappears in the liquefaction of one unit of weight of the substance. (a) Let a number of lbs. of iron required; then, assuming the latent heat of fusion of ice to be 80, 250 x x 2 x 80. vided the pressure is produced by any gas or vapour other than that of the liquid. A liquid always evaporates when its surface is not in contact with its own vapour at its maximum tension for the temperature of the liquid. A liquid boils when its temperature reaches that point at which the tension of its vapour is equal to the pressure to which it is subjected, and which, in the case of a liquid exposed to the air, is the pressure of the atmosphere. The dew-point is the temperature at which the aqueous vapour which always exists in the atmosphere, begins to be deposited in the form of moisture. The dew-point is the same as the temperature of saturation of the aqueous vapour of the atmosphere. 15. When a diverging pencil of light falls on a concave lens, the amount of divergence is increased, so that, after passing through the lens, the rays appear to proceed from a point situated between the actual point of emission and the centre of the lens. A short-sighted person can only see objects distinctly when within a certain distance of the eye. When an object is seen through a concave lens, the pencils of light proceeding from the object appear to diverge, and consequently to proceed, from points nearer the eye. The same effect is consequently produced as if an object nearer the eye were seen by the unaided vision. 16. When a ray of light passes out of a medium, the angle of refraction is greater than the angle of incidence. The limiting angle is that angle of incidence of an emergent ray for which the corresponding angle of refraction is 90°. Suppose B C to be the surface of the water and O the point from which the rays proceed. If AOK is the limiting angle, all rays between OA and OK are partly refracted and partly reflected at the surface of the water. All rays, as OH, lying on the side of OK opposite to O A, undergo total reflection at the surface. |