PROBLEM 9.176 For the right circular cone of Sample Prob. 9.11, determine the value of the ratio a/hfor which the ellipsoid of inertia of the cone is a sphere when computed (a) at the apex of the cone, (b) at the center of the base of the cone. SOLUTION (a) From sample Problem 9.11, we have at the apex A2310xIma=223154yzIImah==+Now observe that symmetry implies 0xyyzzxIII===Using Equation (9.48), the equation of the ellipsoid of inertia is then 2221xyzIxIyIz++=or 22222233131110ma xmahymahz+++For the ellipsoid to be a sphere, the coefficients must be equal. Therefore, 21105
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