A disk and a ring of the same mass are rolling to have the same kinetic energy. What is ratio of their velocities of centre of mass

Options

A. `sqrt4: sqrt3`
B. `sqrt3: sqrt4`
C. `sqrt3: sqrt2`
D. `sqrt2: sqrt3`

Answer

A

Explanation

`K_("disc")= (1)/(2) mv_(d)^(2) (1 + (k^(2))/(R^(2))) = (3)/(4) mv_(d)^(2)` [As `(k^(2))/(R^(2))= (1)/(2)` for disc]
`K_("ring")= (1)/(2) mv_(r ) (1 + (k^(2))/(R^(2))) = mv_(r )^(2)` [As `(k^(2))/(R^(2))=1` for ring]
According to problem `K_("disc") = K_("ring") rArr (3)/(4) mv_(d)^(2)= mv_(r)^(2) rArr (v_(d))/(v_(r ))= sqrt((4)/(3))`