FACULTY OF ARTS. FINAL HONOUR PHYSICS. Electricity and Magnetism. 1. Show that 4πIVXH is an expression of the fact that the work done in carrying unit pole once about a current of strength I is 4π1. 2. Given that the moment of the electro-magnetic momentum due to a pole of strength m and an electric charge e is -μme about the line joining the two, prove that the force on a charged particle moving through a magnetic field is given by e(vXH). 3. Write notes on the following ideas:— (c) Dielectric currents. 4. Thomson, in his experiments on positive rays, always found three types, viz., (1) Undeflected rays, (2) Primary rays, i.e. those-carrying charges while in the deflecting field, and (3) Secondary rays, i.e. those changing their charge while in the deflecting field. (a) Give an account of Thomson's proof that secondary rays may come from either of the other types of ray. (b) How do we know from an examination of the photographs that all secondary rays for each molecular group have nearly the same velocity and how is this fact explained? 5. What is the "Mahomet's Coffin" method of measuring the charge on an ion (H. A. Wilson's method)? (b) What are the reasons for its giving a wrong value? 6. (a) Show how Bragg and Kleeman determined the ranges of the a particles. (b) How is it shown that all the a particles from a given substance are expelled with the same velocity? (c) How is it shown that while 7.06 cm. is the maximum range of an a particle from radium C, the average range is 6.7 cm. (d) Reconcile these facts in (b) and in (c). 7. (a) How has it been established that the average life of a radium atom is 2880 years? Give an account of the measurement. (b) Show how this leads to the estimate that the average life of a uranium atom is of the order of 101o years. FINAL HONOUR PHYSICS. Dynamics of Rigid and Elastic Bodies. 1. What was the great advance in the theory of elasticity made by Green? Explain fully. 2. (a) Show how a homogeneous strain may be resolved into three components, one of which is a pure rotation, the second a dilation or compression, and the third a shear. (b) What are the principal elastic constants? Explain how all may be determined by means of two experi ments. 3. A rectangular parallelepiped has the dimensions a, b, and c. Deduce the equation of the ellipsoid of inertia when the origin is at one corner and find the value of the moment of inertia for an axis passing through this corner making equal angles with the edges of the parallelepiped. 4. A body is fixed at one point but is otherwise free to move. Deduce Euler's dynamical equations of motion for the body. 5. Show that the motion of translation and rotation of a rigid body may be studied independently. FINAL HONOUR PHYSICS. Dynamics. 1. A body moves about a centre so that its potential energy is inversely proportional to the cube of the distance from the centre toward which it is attracted. Obtain the differential equations of motions. 2. Two elements of a cycloid are placed side by side in a vertical plane with the cusp upward. A particle is suspended on a thread at the cusp so that it hangs between the cycloidal arcs. Show that if the thread be of proper length the time of swing of the particle as a pendulum is independent of the amplitude of swing. 3. Show that the necessary and sufficient condition for equilibrium of a particle is that the virtual work on a small displacement is equal to zero. 4. A particle of mass m is acted upon by an elastic force which is proportional to the distance from the mean position, a resisting force proportional to the velocity, and a periodic force. Form the equation of motion, solve it, and find the condition for the maximum excursion of the particle. 5. (a) A flexible inextensible chain is suspended at one end. Form the differential equation of its motion when disturbed and allowed to vibrate with a small displacement. (b) Show that the solution of the equation leads to a Bessel's function and show how to evaluate the coefficients of the series which define the function. |