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FACULTY OF ARTS.
Please arrange the answers in the order of the questions. 1. (a) State that one of Newton's laws of motion which applies to a body moving with variable velocity.
(b) Define the dyne.
(c) Show how observations on freely falling bodies might furnish data for comparing the dyne with the weight of one gram.
2. (a) Explain why a force must be applied to a body in order that it shall move in a circular path at uniform speed.
(b) A child weighing 25 kg. is in a swing, the ropes of which are 2 meters long, and is swinging so that his speed at the middle point of the arc is 5 meters per sec. What is the maximum tension on the ropes?
3. (a) State exactly the result of increasing the pressure on a given quantity of air, the temperature remaining con
(b) In making a barometer a small quantity of air has been left in the space above the mercury The tube used has an inside cross-section of 1 sq. cm. When the true atmospheric pressure is 77 cm. of mercury, this barometer stands at 76, and when the true pressure is 78 it stands at 76.9. What is the true pressure when it stands at 74?
4. How may the speed of sound in air be measured, given a tuning-fork of known frequency and a tube of variable. length?
5. (a) Define boiling.
(b) Explain why boiling occurs at a definite temperature, and why that temperature depends on the atmospheric pressure.
6. In laying steel rails 30 ft. long, how much space must be left between each two, if the temperature at the time be 0°C. adn the maximum summer temperature be 35°C.? Given the coefficient of linear expansion of steel, 0.000011.
7. (a) Define: unit magnetic pole, strength of magnetic field.
(b) Two bar magnets, exactly alike, are 10 cm. long and have poles of strength 50. The magnets are placed in the same line, the north pole of one facing the south pole of the other, and the middle points of the magnets 20 cm. apart. Calculate the net attraction between the magnets.
8. Give an account of an experimental method for cemparing the electrical resistance of two conductors, explaining the theory of the method.
9. (a) Given two convex lenses, of focal length respectively 1 cm. and 5 cm., state how to combine them to form a microscope.
(b) Make a diagram of the arrangement, showing the lenses and the object, and assign suitable numerical values to the various distances.
(c) On the basis of the diagram, calculate the magnifying power of the microscope.
10. Explain either
(a) How the speed of a star toward or away from the earth may be measured.
(b) Why the spectrum of sunlight is crossed by dark
(Three questions to be answered from each part).
1. A fine thread after being wound many times about a cylinder (radius 4 cm. ; mass kg.) has its free end attached to the highest point of a smooth plane inclined to the horizontal at 30°. The cylinder is set on the plane so that the thread unwinds as it rolls down.
Find (a) The angular acceleration, and
(b) The tension of the thread.
The moment of inertia of cylinder about its axis of figure. is Mr3.
2. Show that the radius of gyration of any uniform right prism, about a line perpendicular to its axis and through the middle point of that axis, is equal to the sum of the radius of gyration of the axis of figure plus that of the central cross section of the prism.
3. ABC is a straight bar (mass 40 lb., c. of g. 5 feet from A), AC is horizontal; at A it is hinged to a wall; and at B (4 feet from A) it rests on the rim of a wheel (mass 100 lbs., circumference 4 feet, radius of gyration 1.6 feet). By lifting C the bar is raised off the wheel, which is then set spinning freely at 200 revolutions per minute. The bar is then allowed to rest on the wheel rim for 6 seconds, after which it is raised again. If the coefficient of friction be 0.20, find,
(a) The final angular velocity of the wheel, and
(b) The energy converted into heat at the point C.
4. (a) Show that there are two points in a straight uniform bar about which it will swing with the same period as about either end.
(b) Establish the proposition you use it part (a).
B. Heat and Light.
5. Draw diagrams based on the Principle of Huyghen's for the following case:
For refraction of a plane wave at a plane surface when the light passes from one medium to a second and the ratio of the velocities in the two media is 3 to 2. Prove that the index of refraction is equal to the ratio of the sines of the angles of incidence and refraction.
6. A parallel beam of light falls on a glass prism making an angle of 70° with the surface of the prism. Using 1.55 as the value of the index of refraction and 60° as the angles of the prism, trace the path of this beam through the prism and find the angle between the incident and emerging beams.
7. A weight thermometer consists of a steel tube filled with mercury. The weight of mercury in the tube is 368 grams at 0°C. If the tube and contents are heated to 100°, 4.33 grams run out. The coefficient of linear expansion of steel being .000011, what value does this indicate for the coefficient of cubical expansion of mercury? Density of mercury at 0°C. is 13.59 grm./c.c.
8. Explain the triple point diagram and contrast the diagrams for water and carbon dioxide. What conclusion regarding the liquid state of the latter substance may be drawn?
9. Show that the magnetic intensity at a point along the line of the axis of a bar magnet, r cm. from its centre, is
magnet (r is large compared with the length of the magnet).
10. (a) Explain how lightning rods may be a source of protection to buildings.
(b) What precautions should be insisted upon in their erection?
(c) What is meant by the term "hysteresis" when used in connection with the magnetization of iron?
(d) Describe generally the form of curve which gives the relation between the magnetic induction, and the magnetizing force in soft iron.
11. (a) Define unit magnetic pole and unit electrical current in the electromagnetic system, and state the relation of the ampere to the latter.
(b) At a place where the value of H is 0.16, the angle of deflection of a tangent galvanometer, when a certain current is sent through it, is 60°. The galvanometer consists of 20 turns of wire of 25 cm. mean radius. What is the strength of the current in amperes?
12. (a) At a place where the angle of dip is 60°, the horizontal intensity of the earth's magnetic field is 0.15. What is the e.m.f. in volts, induced in a car axle of 120 cm. length, moving with a horizontal linear velocity of 1 kilometres per minute?