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Q. The radius of gyration about an axis through the center of a hollow sphere with external radius a and internal radius b is

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The radius of gyration about an axis through the center of a hollow sphere with external radius a and internal radius b is

Solution:

As we know moment of inertia of a hollow sphere with external radius $a$ and internal radius $b$ is

$I=frac{2}{5} Mleft(frac{a^{5}-b^{5}}{a^{3}-b^{3}}right)$

Radius of gyration, $K=sqrt{frac{I}{M}}$

where, $M=$ mass of sphere.

so, $ K=frac{sqrt{frac{2}{5} Mleft(frac{a^{5}-b^{5}}{a^{3}-b^{3}}right)}}{M}$

$Rightarrow K=sqrt{frac{2}{5}left(frac{a^{5}-b^{5}}{a^{3}-b^{3}}right)}$

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