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N.B.-Only 14 questions to be answered.
1. Enunciate and prove the polygon of forces. Is the converse true? Why?
2. Prove that a system of forces acting in one plane on a rigid body will be in equilibrium if the algebraical sum of the forces resolved parallel to two fixed straight lines in the plane vanishes, and the algebraical sum of the moments round any point in the plane also vanishes.
3. A man carries a bundle at the end of a stick over his shoulder: if the portion of the stick between his shoulder and his hand be shortened, how will the pressure on his shoulder be altered? Will his pressure on the ground be altered? Explain your answers.
4. A body of 50 kilograms hangs at rest, and is supported by two strings whose lengths are 1.5 m., and 2 m. The other ends of the strings are fastened at two points in a horizontal line 2.5 m. distant from one another; find in dynes the tension of each string. g = 980.
5. Enunciate Kepler's laws of planetary motion, and give the mathematical deductions from each.
6. Explain the floating of a needle on the surface of water. Why can ships built entirely of iron float in water?
7. Define diffusion. What are the differences between the diffusion of gases and liquids?
8. Explain fully the accumulation of electricity in a Leyden jar.
9. What is meant by saying that electricity resides only on the external surface of a conductor? Describe two experiments to prove this.
10. Determine the relation between the energy, capacity, and potential of a charged conductor.
11. What is atmospheric electricity? How is it produced? How is it measured ?
12. Describe induction in Voltaic electricity. Describe the construction of an electromagnet.
13. What are lines of magnetic force? How may they be determined in any magnetic field? Describe a convenient experiment to trace the lines of magnetic force around an ordinary magnet.
14. Describe the construction and use of a syren.
15. Explain the production of acoustic beats. What important fact regarding beats has Helmholtz proved?
16. What relation must exist between the length of an organ pipe and the note produced by it? Calculate the length for the note C(= 256).
1. Prove that the sum of the products of the mass of each particle of a material system into the square of its distance from any point exceeds the sum of the products of the mass of each particle into the square of its distance from the centre of mass by the product of the sum of the masses into the square of the distance between the point and the centre of mass.
2. A body whose mass is 10 kilograms draws another body of 20 kilograms by means of a stretched rope along a rough horizontal plane. If the coefficient of friction be, find (1) the tension of the rope, (2) the motion of the centre of mass,
3. Prove that the effect of friction (angle of repose ε) on a screw of angle a is to make the mechanical advantage the same as that of a frictionless screw of angle a+, according as P is just overcoming W or W overcoming P.
4. If the coefficient of friction between a rope and a cylinder be 0.5, and a man can exert a force equal to the weight of 100 kilograms, what force could he balance with 4 turns of the rope? Given log. e = 0·4342925.
5. Deduce the formula t = π
the oscillation of a simple pendulum.
(1+sin2 a) for
6. Prove that in an atmosphere of uniform temperature the pressure decreases in G. P. as the altitude increases in A. P.
7. Find the hodograph of a planet's motion, and deduce therefrom the apparent path of a star on account of aberration.