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I got the same result (i.e. same force at their respective surfaces for same masses and radii, and your value also.) The sphere, of course is easy!!!! Every text does it. Note: earlier versions of Marian do it for the potential. After taking the grad, I didn't believe the answer and continued my search.
See my recent post.
bc
ps. Congrats to Michael, another doubter.
Michael Bowen wrote:
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