Re: Saturday Morning Puzzle (was: Sunday Morning Puzzle.)

[Michael Bowen <fizzbowen@MINDSPRING.COM>]

At 22:38 2001/10/05, Bernard Cleyet wrote:
> Last week brian w. suggested that a disk of the same mass and radius as
> a sphere would have a greater attractive force at the center of its face
> (toward the sphere on the pendulum).  Rather than stick my neck out, I
> pose the Sat. morn. question.  (Since most of you won't read this 'till
> then.)
>
> What are the respective g fields at the surface of a sphere of radius R
> and the center of a face of a disk also radius R and length 4/3 R.
> (These better have the same volume, or I'm dead!)
>
> Express in terms of rho (volume density), R, and G
>
> P.s. If you don't want to do the triple integration for the cylinder,
> the formula is in the solutions book for the latest ed. of Marian.

Sorry, I don't have the latest ed. of Marian, only a very old one, but I
couldn't resist the challenge, so I did the triple integration by hand. At
least I think I did.
My answers for g turn out to be ... (don't scroll down if you don't want to
see them yet)












































... the same for both shapes, namely, 4 * pi * G * rho * R / 3

I will not be (too) chagrined if someone tells me I didn't do the triple
integral on the cylinder correctly. I can always claim that it was late at
night when I worked it out. :-)

--MB