1. A spherical nuclear reactor of mass 1030 kg in interstellar space is completely surrounded by a thin, nonrigid spherical shell of matter with a mass of 1026 kg (see the figure) The reactor loses 101° kg/sec of its mass by the emission of electromagnetic radiation. (If this sounds like the description of a star, it's no accident!) This radiation is completely absorbed by the surrounding shell of matter. What must be the radius of the spherical shell if the repulsion exerted on it by the radiation is just great enough to balance the gravitational attraction exerted on it by the reactor? (Consider the forces exerted on a small portion of the shell.)
2. In the Michelson-Morley experiment of 1887, the length 1 of each arm of the interferometer was 11 m, and sodium light of wavelength 5.9x10 m was used. The experiment would have revealed any fringe shift larger than 0.005 fringe. What upper limit does this place on the speed of the earth through the supposed ether?
3. The ether-wind theory of the Michelson-Morley experiment is discussed in the text for the special case where the arms of the interferometer are parallel and perpendicular to the wind. Consider the general case for an angular setting 19 as shown (see the figure). Prove that, for equal arms of length 1, the time difference for the two paths is given to a good approximation by
4. A Michelson interferometer for sound waves is made with a loudspeaker as source, a microphone as detector, a thin sheet of paper as beam splitter, and two pieces of board as mirrors (see the figure). The arms of the interferometer are of equal length 1, and the whole apparatus can be rotated. A wind, constant in speed and direction, blows past the apparatus. Once every second the speaker emits a very brief pulse of sound. Answer the following questions, using the result of Problem 2-8.
(a) In most orientations of the interferometer the echo received by the microphone consists of two pulses in quick succession. Why?
(b) At certain orientations of the interferometer the time delay between the two echoes is maximum. How many such orientations are there in one complete revolution of the apparatus? In relation to the direction of the wind, what are these orientations?
(c) If the length of each arm of the interferometer is 3 m, and the maximum time delay be¬tween echoes is found to be le sec, what is the speed of the wind? Sound waves travel with a constant velocity relative to the air. Take the magnitude of this velocity to be 300 m/sec.