A thin hollow cylinder open at both ends and weight `5 kg` (i) slides with a speed of `5m//s` without rotating and (ii) rolls with the same speed without slipping. Compare the `KE` of the cylinder in the two cases.

Explanation

Here, `m = 5 kg, v = 5 m//s`
(i) Translational `K.E. = (1)/(2)m v^(2) = (1)/(2) xx 5 xx 5^(2)`
`= 62.5 J`
(ii) When the cylinder rolls with the same speed
total `K.E. = K.E.` of translation `+ K.E.` of rotation
`= 62.5 J + (1)/(2)I omega^(2) = 62.5 + (1)/(2)(mr^(2)) (v^(2))/(r^(2))`
`= 62.5 + (1)/(2) xx 5 xx 5^(2) = 125 J`