Find the gravitational attraction of a solid hemisphere of radius a anddensity1 on a unit point mass placed at its pole.(adsbygoogle = window.adsbygoogle || []).push({});

My attempt:

Obviously I figured that spherical coordinates would work nicely for this problem.

I decided to invert the hemisphere thus placing the pole on the origin. Then I decided to split the upside down quarter disc into two integrals. The first integral was then for a cone shaped figure (r1 in the picture i made).

I set it up as follows

[itex] G \int_{\vartheta=0}^{2\pi} \int_{

\varphi=0}^{\pi/3}\int_{\rho=0}^{a/sin(\phi)} sin(\phi)cos(\phi)d\phi d\rho d\theta[/itex]

Plz let me know if i have made any mistakes with the above integrand (pi/3 is where a cone will intersect a circle of equal radius).

However I could not manage to think up the equation (in spherical coordinates) for the lower circular bound. I considered changing coordinate systems for the outer spherical part but setting up the equation for force of gravity might have been tricky. Any help will be greatly appreciated.

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# Homework Help: Gravitational attraction of a hemisphere at its pole

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