A solid disc first rolls without slipping and then slides without rolling down the same inclined plane. The velocities in two cases at the bottom are in the ratio of

Options

A. `1:2`
B. `2:sqrt(6)`
C. `sqrt(6):3`
D. `sqrt(3):1`

Answer

B

Explanation

`(1)/(2)mv_(1)^(2)+(1)/(2)Iomega^(2)=mgh`
`(1)/(2)mv_(1)^(2)+(1)/(2)xx(1)/(2)mr^(2)omega^(2)=mgh`
`(1)/(2)mv_(1)^(2)+(1)/(4)mv_(1)^(2)=mgh`
`(3)/(4)mv_(1)^(2)=mghimpliesv_(1)=sqrt((4gh)/(3))`
When the disc slides then
`(1)/(2)mv_(2)^(2)=mghimpliesv_(2)=sqrt(2gh)`
`therefore (v_(1))/(v_(2))=(sqrt((4gh)/(3)))/(sqrt(2gh))=sqrt((4)/(6))implies(v_(1))/(v_(2))=2:sqrt(6)`