If a disc of mass m and radius r is reshaped into a ring of radius`2r`, the mass remining the same, the radius of gyration about centrodal axis perpendicular to plane goes up by a factor of

Options

A. `sqrt(2)`
B. 2
C. `2 sqrt(2)`
D. 4

Answer

C

Explanation

The radius of gyration, `K_(D)=sqrt((I_(D))/(m))=sqrt(((1)/(2)mr^(2))/(m))=(r)/(sqrt(2))`
`K_(R)=sqrt((I_(PR))/(m))=sqrt((m(2r)^(2))/(m))=2r`
`:. (K_(R))/(K_(D))=2 sqrt(2)`.