68. A weight of 4 pounds hung on a spiral spring draws it out by 3 inches. Find the period of vibration for a weight of 7 pounds hung on the same spring. The inertia of the spring is neglected. [By Hooke's law elongation produced by 7 lbs. 7 × 3 21 inches. 4 4 VISCOSITY AND CAPILLARITY. 69. State the theories of capillary action given by Laplace and Thomas Young. Adopting the theory of the latter, find the height to which water will rise in a clean glass tube mm. in diameter. Suppose the tube wetted with water, and take the surface tension of water as 3 grains weight per lineal inch. [Laplace assumes that the liquid has uniform density; and that the attraction of its molecules is sensible only at insensible distances. Young founded his theory on the principle of surfacetension. The forces are of two kinds :-attraction and repulsion. The former is constant at small distances, and extends further than the latter, but the latter increases rapidly as the distance diminishes. 2 Wh=where W is weight per unit bulk, h height T liquid rises in tube, 7 tension of liquid, and r the radius of tube. 70. Find the pressure inside a spherical soap bubble of four inches diameter, taking the outer atmospheric pressure as 30 inches of mercury and the tension of each of the liquid surfaces as 3 grains weight per lineal inch (one cubic inch of mercury weighs 3437 grains). [Let p be the excess of pressure inside the bubble over the outside pressure, and the tension per unit length, then, since there are two free surfaces, But pressure outside bubble ... --30 inches of mercury per sq. inch Total pressure inside soap bubble 30 x 3437+6 7000 pounds per sq. inch 14731 pounds per sq. inch.] 71. Find the depression of mercury in a capillary tube of glass 1 inch diameter. (Suppose T12 grains per inch, and air angle between mercury and glass 45. The weight of one cubic inch of mercury is 3437 grains.) [Let h depression, then SOUND. 72. The velocity of sound in air at 0° C. is 1093 feet per second. Calculate the velocity at 10° C. 73. Find the velocity of sound at 0° C. in carbonic acid gas, the density of which compared with air taken as unity is 1.53. The bulk for one additional atmosphere of pressure. density of mercury is 18.8 times that of ether. Find the velocity of sound in ether. 75. A pianoforte wire weighing 0023 of a pound per foot is stretched between two points 10 feet distant with a tension equal to the gravity of 100 lbs. Find the lowest fundamental note of the wire. [If n be the number of vibrations it makes per second, 76. The extremities of the prongs of a tuning fork which executes 256 periods per second have a range on each side of their position of equilibrium of half a centimetre. Find their maximum velocity. [Letv be their maximum velocity. 77. Define Height of the Homogeneous Atmosphere. Write down the Newtonian formula for the velocity of sound in a gas. Find the velocity of sound in hydrogen for which the height of the homogeneous atmosphere at 0° C. is 147 x 26000 feet. [Newtonian velocity of sound in a gas is the velocity acquired by a body falling through half the height of a homogeneous atmosphere of that gas where g-force of gravity; h=barometric height; 8 density of mercury; d=density of gas. Velocity of sound in hydrogen =√32·2 × 14·7 × 26000 feet per second LIGHT. 78. Explain what is meant by dispersion and by diffraction of light. 79. Describe very carefully the appearance of the prismatic spectrum of the electric light, and the arrangement necessary for producing a pure spectrum. 80. Explain the colour of objects. Describe and explain the appearance presented by objects of different colours when viewed by mono-chromatic light. 81. Give diagrams to explain refraction on the emission theory of light, and on the undulatory theory. Deduce a conclusion which furnishes a crucial experimental test between the two theories, and give the result of the experimental investigation. 82. Taking the index for refraction from air into water as 1.34, and the angle of incidence of a ray of light as 35°, find the angle of refraction. [Let i be the angle of refraction. 83. Taking the velocity of light in air as 186000 miles per second, and the mean refractive index for light passing from air into water as 1:336. Calculate the velocity of light in water. Calculate also the period of vibration of an ether particle for light of 207 inch, propagated in vacuum. 107 wave length |