5. The optical apparatus in a revolving lighthouse weighs one ton. It is supported on a vertical cylinder (2 feet diameter and mass 500 lbs.). In order to relieve the vertical force on the conical pivot on which the whole turns, the drum is placed in a cylindrical well giving 1/5 inch clearance at the sides and 2/5 inch clearance at the bottom, and mercury is poured in to partially float the load. Taking the density of mercury as 840 lb. per cubic foot, find how many cubic inches of mercury will be required if the force on the pivot is to be reduced to 100 lb. wt.

6. A square table of mass 40 lb. has legs at each corner, A, B, C and D. The length of a side is 5 feet. A 10 lb. stone lies at a point 2 feet from AB and 1 foot from AD.

(1) Find the difference in the forces between floor and table legs at A and C.

(2) Show that it is impossible to find the values of the individual forces A, B, C and D.

7. A cog wheel is keyed to a shaft and when viewed in the light of an arc lamp alternating 120 times per second, the cogs appear to be at rest. The key, however, is seen to make 2 revolutions per second.

(a) Find the least number of cogs that the wheel may have.

(b) A second wheel of 25 cogs is driven from the first. Find its angular velocity, and show that its cogs too will appear to be at rest.

FACULTY OF APPLIED SCIENCE.

PHYSICS IB.

Please arrange the answers in the order of the questions. 1. (a) Define the terms: wave-length, stationary wave, node.

(b) How may stationary waves be set up?

(c) Show that the distance between nodes, in a stationary wave, is one-half the wave-length.

2. (a) Define: magnifying power of a telescope.

(b) A telescope is used to look at a double star. Make a diagram showing the path of the rays through the instrument, and explain how the images are formed.

(c) If the focal lengths of objective and eyepiece are 1 metre and 5 cm. respectively, find the magnifying power of the telescope, and its length when focussed on a distant object.

3. (a) Define the terms: calorie, British thermal unit, latent heat of fusion.

(b) If the latent heat of fusion of ice is 80 calories per gram, express it in terms of pounds and British thermal units.

4. Either (a) Describe an experiment showing that the melting-point of ice depends on the pressure. Is the meltingpoint lowered or raised, by increase of pressure?

or (b) Describe the experiment in which water was made to freeze while boiling. What principles are illustrated by this experiment?

5. (a) Define: unit magnetic pole.

(b) In what unit is the strength of a magnetic field measured?

(c) If the horizontal component of the earth's magnetic field be 0.2, and the angle of dip 60°, find the total field, and the vertical component.

6. (a) Define: electrical capacity of a conductor.

(b) How is the capacity affected by bringing up another conductor connected to the earth?

(c) Explain this effect.

7. (a) State Ohm's law.

(b) Use it to prove that a current divides itself between two conductors in parallel, in the inverse ratio of their resistances.

8. A battery of 60 storage cells in series is used to light 50 incandescent lamps in parallel. Given the resistance of each cell 0.003 ohm, the electromotive force of each cell 2.1 volts, the resistance of each lamp 220 ohms, and the resistance of the line from the battery to the lamps 0.46 ohm, find

(a) the current flowing through the battery;

(b) the power delivered by the battery to the line; (c) the power delivered by the line to the lamps.

PHYSICS II.

1. The pendulum of a clock consists of a steel tube 2 ft. 6 inches long which weighs 2 lbs.. At the lower end of the tube is fastened a steel cylinder 6 inches long and weighing 8 lbs. whose moment of inertia about a transverse axis through its centre is .15 units. The end of the steel tube is fastened centrally on the end of the cylinder so that their axes are in the same line.

(a) Calculate the radius of gyration of the system when suspended on a knife edge 3 inches from the upper end of the tube.

(b) The position of centre of gravity of the system.

(c) The period of vibration when swinging through a small arc.

2. A stamping machine has a fly-wheel weighing 966 lbs. made in the form of a solid disc 2 ft. in diameter. An operation of the machine occurs once in 3 seconds. If the ma

chine requires H.P. to drive it and 15 per cent. of the energy supplied is wasted in friction, etc., how much will the speed of the fly-wheel fluctuate if the upper limit is 180 R.P.M.?

3. A spiral spring requires a force of 3 lbs. to stretch it one inch.

(a) With what period will it oscillate vertically if loaded with a 5 lb. weight?

(b) If the 5 lb. load is hung on the spring when it is unstretched and dropped, dropped, what will be the maximum. stretch of the spring?

(c) Show how to calculate the energy stored in the spring in terms of the stretch.

4. Show that the contractile force developed in a bar of length of cross-sectional area a when the bar is held rigidly at the ends and cooled from a temperature t2 to temperature t1 is F-Eac (t2-t,) where E is the value of Young's Modulus and c is the coefficient of expansion.

5. A wagon wheel whose radius of gyration is the radius of the wheel rolls down an incline of 20° on to a horizontal plane. It travels 60 ft. in 5 seconds on the horizontal. If the incline is 8 ft. long, with what initial angular velocity did it start down the plane?

6. The angular twist in a bar held rigidly at one end and twisted by a torque L at the other is a=Ll/In.

(a) Explain the exact significance of each symbol in the expression and in what units each should be measured and why.

(b) What H.P. is being transmitted by a line of steel shafting, 2 inches in diameter and 60 ft. long, for which the rigidity is 9000000 lbs. per sq. inch when running at 120 R.P.M. and the angular distortion is 2°?

7. (a) A hollow sphere whose external and internal radii are 12 inches and 18 inches respectively is placed on a horizontal plane where the coefficient of friction between it and the plane is .3. Calculate the maximum horizontal acceleration which may be given to the plane and have no slipping between the sphere and the plane.

(b) Would this acceleration be changed if instead of moving horizontally the plane be kept horizontal and moved in a direction inclined to the horizontal? Explain your answer by showing what change would result, and why.