A hollow cylinder open at both ends slides without rotating, and then rolls without slipping with the same speed. The ratio of the kinetic energy in the two cases is (taken in order)

Options

A. `1 : 1`
B. `1 : 2`
C. `2 : 1`
D. `1 : 4`

Answer

B

Explanation

`KE_(1)=(1)/(2)mv^(2)`
`KE_(2)=(1)/(2)mv^(2)+(1)/(2)l omega^(2)`
`= (1)/(2)mv^(2)+(1)/(2)(mr^(2))((v^(2))/(r^(2)))=mv^(2)`
`rArr (KE_(1))/(KE_(2))= +((1)/(2)mv^(2))/(mv^(2))=(1)/(2)= 1:2`.