Bodies of regular geometrical shape were allowed to roll on a horizontal surface. It was found that for one rolling body, die translational KE was equal to rotational KE, the body must be

Options

A. a solid sphere
B. a hollow sphere
C. a disc
D. a thin ring

Answer

D

Explanation

Given : Translational K.E. = Rotational K.E.
`(1)/(2)mv^(2)=(1)/(2)Iomega^(2)`
But `I=mK^(2) and omega^(2)=(v^(2))/(R^(2))`
`therefore" "(1)/(2)mv^(2)=(1)/(2)mK^(2).(v^(2))/(R^(2))`
`therefore" "(K^(2))/(R^(2))=1" "therefore K=R`
This is possible only for a ring, for which
`I=mR^(2)=mK^(2) or R= K`