If a disc of mass m and radius r is reshaped into a ring of radius 2r, the mass remaining the same, the radius of gyration goes up by a factor of :

Options

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

Answer

C

Explanation

For disc `(1)/(2)mr^(2)=mk_(1)^(2)impliesk_(1)=sqrt((1)/(2))r`
For ring `m(2r)^(2)=mk_(2)^(2)" "k_(2)" "2r`
`therefore (k_(2))/(k_(1))=(2r)/(sqrt((1)/(2)r))=2sqrt(2)`