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Center of mass on the edge Consider the constant-density
Chapter 14, Problem 62E(choose chapter or problem)
Center of mass on the edge Consider the constant-density solid \(\{(\rho, \varphi, \theta): 0<a \leq \rho \leq 1,0 \leq \varphi \leq \pi / 2,0 \leq \theta \leq 2 \pi\}\) bounded by two hemispheres and the xy-plane.
a. Find and graph the z-coordinate of the center of mass of the plate as a function of a.
b. For what value of a is the center of mass on the edge of the solid?
Questions & Answers
QUESTION:
Center of mass on the edge Consider the constant-density solid \(\{(\rho, \varphi, \theta): 0<a \leq \rho \leq 1,0 \leq \varphi \leq \pi / 2,0 \leq \theta \leq 2 \pi\}\) bounded by two hemispheres and the xy-plane.
a. Find and graph the z-coordinate of the center of mass of the plate as a function of a.
b. For what value of a is the center of mass on the edge of the solid?
ANSWER:Solution 62E1. The coordinates of the center of mass of the given soli