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# mid3_sol - Name Student ID S10 PHY321 Midterm 3 NOTE Show...

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Name: Student ID: S10 PHY321: Midterm 3 April 16, 2010 NOTE: Show all your work. No credit for unsupported answers . Moreover, the work can earn you credit for problems that are not fully completed! Turn the front page only when advised by the instructor! Total points for this exam: 25 Useful formulas can be found at the end of this exam.

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1. A spherical planet of radius R has a density that is largest in its center and decreases with distance r from the center as ρ ( r ) = B ( R 2 - r 2 ), where B is a constant with the appropriate units. (a) [3 pts] Determine the mass of the planet in terms of B and R . (b) [2 pts] Use the shell theorem to find the gravitational field at distance r R . (c) [3 pts] Use the shell theorem to find the gravitational field at distance r R . Check whether the answers for (1b) and (1c) agree at r = R . (d) [4 pts] Use your answer to part (1c) and the differential form of Gauss’ law ( ~ ∇· ~g ( ~ r ) = - 4 πGρ ( ~ r )) to derive the original density.
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mid3_sol - Name Student ID S10 PHY321 Midterm 3 NOTE Show...

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