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 K.E. ")/("Translational K.E.") =((1)/(2) Iomega^(2))/((1)/(2) mv^(2)) =((mK^(2))(v^(2))/(R^(2)))/(mv^(2))=(K^(2))/(R^(2))`