Two identical cylinders 'runa race' starting from rest at the top of an inclined plane, one slides without rolling and other rolls without slipping. Assuming that no mechanical energy is dissipated in heat, which one will win ?

Explanation

When a cylinder slides without rolling,
`E = (1)/(2)m'upsilon^(2) , upsilon'^(2) = sqrt(2E//m)`
When the cylinder rolls without slipping
`E = (1)/(2)m upsilon^(2) + (1)/(2)I omega^(2)`
`= (1)/(2)m upsilon^(2) + (1)/(2) ((1)/(2)m r^(2)) omega^(2)`
`= (1)/(2) m upsilon^(2) + (1)/(4)m upsilon^(2) = (3)/(4)m upsilon^(2)`
`:. upsilon = sqrt((4E)/(3m))`
As `upsilon' gt upsilon`, therefore sliding cylinder will with the face.