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The glass is most stable with about 183.5 grams of water.
The center of gravity of a system is the weighted mean center of gravity of its components.
The first component is the glass, with mass 100 g at a distance 8 cm
The second component is the water of depth x. Its mass is pi*4^2*x = 50.265x cm. The distance from the rim is 15 - x/2.
The weighted mean (center of gravity) is given by the formula:
C.G.= [100*8 + 50.625x(15 - x/2)]/[100 + 50.265x]
Since this is measured from the rim, we want to maximize this. My TI-83 gives x=3.651 as the depth corresponding to a mass of 183.5
Interesting to note is that the center of mass is right at the top of the water line in this situation. |
