A solid sphere of mass m and radius R is rotating about its diameter A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere . The ratio of their kinetic energies of rotation `(E_("sphere") // E_("cylinder"))` will be

Options

A. `2 : 3`
B. `1 : 5`
C. `1 : 4`
D. `3 : 1`

Answer

B

Explanation

`(E_("Sphere"))/(E_("Cylinder")) = ((1)/(2) I_(s) omega_(s)^(2))/((1)/(2) I_(c) omega_(c)^(2)) = (I_(s) omega_(s)^(2))/(I_(c) omega_(c)^(2))`
Here , `I_(s) = (2)/(5) m R^(2) , I_(c) = (1)/(2) mR^(2) , omega_(c) = 2 omega_(s)`
`(E_("Sphere"))/(E_("Cylinder")) = ((2)/(5) mR^(2) xx omega_(s)^(2))/((1)/(2) mR^(2) xx (2 omega_(s))^(2)) = (4)/(5) xx (1)/(4) = (1)/(5)`