A concave astronomical telescope mirror may be made by rotating a circular tank of mercury. Find an expression for the shape of the surface in terms of the density of mercury, the radius from the centre and the rotaion rate(adsbygoogle = window.adsbygoogle || []).push({});

so far ive come up with:

KE=1/2MV^2

In the case of circular motion the relation v = ωr holds, hence

KE=1/2MW^2R^2

The gravitational potential energy is given by

potential energy= mgh

where g is the acceleration of gravity and h is the height of the mercury's surface above some arbitrary elevation, for instance, we can set h = 0 to be the lowest mercury surface.

We set the potential energy equal to the kinetic energy to find the mirror's shape:

H=(1/2g)W^2R^2

which is by definition a parabola

im unsure how to include a density term into this formula any help appreciated

Thanks.

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# Homework Help: Liquid mirror problem

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