The ratio of the radii of gyration of a hollow sphere and a solid sphere of the same radii about a

Options

A. `sqrt((7)/(3))`
B. `(5)/(sqrt(21))`
C. `sqrt((21)/(5))`
D. `(25)/(9)`

Answer

B

Explanation

Hollow sphere, `K_(H)=sqrt((I)/(m))=sqrt(((2)/(3)mR^(2)+mR^(2))/(m))=sqrt((5)/(3))R`
Solid sphere, `K_(S)=sqrt((I)/(m))=sqrt(((2)/(5)mR^(2)+mR^(2))/(m))=sqrt((7)/(5))R`
`:. (K_(H))/(K_(S))=sqrt((25)/(21))=(5)/(sqrt(21))`.