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Physics 341: Problem Set #1 due September 14 You are encouraged to work in groups on these problems, but each student must write up the solutions individually. You must also list your collaborators on your solutions, and cite any external sources you used (other than the course notes or textbook). I will give partial credit for partial answers, but only if you show your work and explain your reasoning. Be careful with units. 1. (a) Use dimensional analysis to derive a relationship between the total mass of a gravitationally bound system M , its typical size R , and the typical speed v of its components. (b) A globular cluster has about 10 6 stars in a sphere of radius 10 pc. Using your analysis above, estimate the speed with which the stars move inside the cluster, in units of km s - 1 . You will need to make an assumption about the average star; be sure to state any assumptions explicitly. (c) Now estimate the mass of a galaxy like the Milky Way, based on the fact that
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