A body rolls without slipping. The radius of gyration of the body about an axis passing through its centre of mass is `K`. The radius of the body is `R`. The ratio of rotational kinetic energy to translational kinetic energy is.

Options

A. `(K^(2))/(R^(2))`
B. `(R^(2))/(K^(2)+R^(2))`
C. `(K^(2))/(K^(2)+R^(2))`
D. `(K^(2)+R^(2))`

Answer

A

Explanation

`("Rotational" KE)/("Translational"KE)=(1/2lomega^(2))/(1/2mv^(2))`
`=(mk^(2)(v^(2))/(r^(2)))/(mv^(2))=(K^(2))/(R^(2))`