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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 righthand 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
 CHAN
 mechanics

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