A uniform rod of length `l` and mass `m` is hung from, strings of equal length from a ceiling as shown in figure. Determine the tensions in the strings?

Options

A. The time after which the ring will start pure rolling is `2` sec if `v` is `20 m//s` and `mu` is `0.5`
B. The time after which the ring will start pure rolling is `2` sec if `v` is `10 m//s` and `mu` is `0.25`
C. The time after which the ring will start pure rolling is `4` sec if `v` is `20 m//s` and `mu` is `0.5`
D. frication will change its direction if `v = 20 m//s` and `mu = 0.5`

Answer

A, B

Explanation

Suppose velocity of ring.

When it starts pure rolling is `v'`. Angular moementum is constant about point of contact as there is no external torque acting about it. Thus
`m.v.R = m.R^(2)((v')/(R)) + mv'R`
`rArr v' = (v)/(2)m//s`
using `v = u + at`
`v' = v + (-mu xx g)t rArr t = (v)//(2mug)`sec.