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Unformatted text preview: PHY 3221: Mechanics I Fall Term 2010 Midterm Exam 2, October 27, 2009 This is a closed book exam lasting 50 minutes. Since calculators are not allowed on this test, if the problem asks for a numerical answer, answering 2 + 2 is as good as 4, and 2 is as good as 1 . 4142 ... . There are four problems worth a total of 20 pts. All four problems appear on the second page of this test. Begin each problem on a fresh sheet of paper. Use only one side of the paper. Avoid microscopic handwriting. Put your name, the problem number and the page number in the upper right-hand corner of each sheet. To receive partial credit you must explain what you are doing. Carefully labelled figures are important! Randomly scrawled equations are not helpful. Draw a box around important results (or at least results which you think might be im- portant). Good luck! 1 Problem 1. [4 pts] In Einsteins theory of general relativity the Schwarzschild radius R s is the radius at which a spherical body (such as a star or a planet) would become a black hole. For example, if you take a star of mass M and squeeze all of its matter within a sphere of radius R s (or smaller), the gravitational pull on the surface becomes so strong that even light cannot escape from it, and the star becomes a black hole. Knowing nothing about general relativity, use dimensional analysis to derive a formula for the Schwarzschild radius R s in terms of the mass of the star M , Newtons gravitational constant G and the speed of light c . Solution. First figure out the units of the relevant quantities: [ R s ] = L, [ M ] = M, [ G ] = L 3 M- 1 T- 2 , [ c ] = LT- 1 . Then write R s M G c from where [ R s ] = [ M ] [ G ] [ c ] L = M L 3 M- T- 2 L T- giving three equations for , and : 1 = 3 + , 0 = , 0 = 2 ....
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This note was uploaded on 12/15/2011 for the course PHY 3221 taught by Professor Chan during the Spring '08 term at University of Florida.
- Spring '08