Question

The radius of gyration about an axis through the center of a hollow sphere with external radius $a$ and internal radius $b$ is (A) \( \sqrt{\frac{2}{5}\frac{(a^{3}-b^{3})}{(a^{5}-b^{5})}} \)

• A. \( \sqrt{\frac{1}{4}\frac{(a^{4}-b^{4})}{(a^{2}-b^{2})}} \)
• B. \( \sqrt{\frac{1}{2}\frac{(a^{5}-b^{5})}{(a^{3}-b^{3})}} \)
• C. \( \sqrt{\frac{2}{5}\frac{(a^{5}-b^{5})}{(a^{3}-b^{3})}} \)
• D. \( \sqrt{\frac{5}{2}\frac{(a^{4}-b^{4})}{(a^{2}-b^{2})}} \)
• E.

Hint:

Put \(b=0\) → solid sphere, \(b=a\) → thin shell case.

Answer 1

The Correct Option is D