A child is on a merry-go-round, standing at a distacne 2 m from the centre. The coefficient of static friction between the child and the surface of merry-go-round is `0.8.` At what maximum angular velocity can the merry-go-round be rotated before and child slips? (Take,` g = 10 m//s ^(2))`

Options

A. `0.5 rad//s`
B. `1 rad//s`
C. `2 rad//s`
D. `4 rad//s`

Answer

C

Explanation

At critical speed, centrifugal force on child must be equal to maximum static friction `m omega ^(2)r = mu V`
where raadius, `r = 2m,`
coefficient of static friction `mu=0.8 and M =` mass of child.
Reaction force, N = mg
So, ` m omega ^(2) r = mu mg implies omega = sqrt((mug)/(r))`
`omega = sqrt((0.8 xx10)/(2)) implies omega =2 rad //s`