A body rolls down a smooth inclined plane. If its rotational kinetic energy is `40%` of its translational K.E., then the body must be a

Options

A. cylinder
B. ring
C. solid sphere
D. solid disc

Answer

C

Explanation

Given : Rotational K.E. `=(4)/(10)` (Translational K.E.)
`therefore (1)/(2)Iomega^(2)=(4)/(10).(1)/(2)Mv^(2)`
`therefore" "(1)/(2)(MK^(2)).(v^(2))/(R^(2))=(1)/(2)((2)/(5)Mv^(2))" "therefore (K^(2))/(R^(2))=(2)/(5)`
`therefore" "K^(2)=(2)/(5)R^(2)" for a sphere "K^(2)=(I)/(M)=(2)/(5)R^(2)`
`therefore" The rolling body is a sphere."`