- #1
sr-candy
- 15
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Homework Statement
A uniform solid consist of a hemisphere of radius r and a right circular cone of base radius r fixed together so that their planes are coincident. If the solid can rest in equilibrium with any point of the curved surface of the hemisphere in contact with a horizontal plane, find the height of the cone in terms of r. [Hint: The center of gravity of the cone is 1/4 its height from the plane face, and the center of gravity of the hemisphere is 3/8 its radius from the plane face.]
Homework Equations
Xcm = (m1x1 +m2x2+...)/summation of m
The Attempt at a Solution
i tried to prove that at any point of the curved surface contacted with the ground, the volume of the left is equal to the right, but then i am having trouble in finding the volume of the varying parts.
another way that i am thinking is that, consider the CG of the cone and hemisphere separately, but again, i can't find the distance of the CGs relative to my reference point
in fact, i am not quite sure about the condition for this system to be at equilibrium
P.S. sry for my poor english as it is not my first language