A rotor is rotating with a constant angular velocity `omega` about its own axis. At the centre of the rotaor a spring is fixed of natural length `(l_(0))` whose other end is connected to a block of mass m. Find the minimum vaule of coefficient of friction between block and rotor wall for which spring remains horizontal. The radius of rotor is `R (R lt l_(0))`.

Options

A. `mu = (mg)/(m omega^(2) R + K (l_(0) - R))`
B. `mu = (mg)/(K (l_(0) - R))`
C. `mu = (mg)/(m omega^(2) R - K (l_(0) - R))`
D. `mu = (mg)/(KR)`

Answer

A

Explanation

`- k Delta x + N = mR omega^(2)`
`Delta x = l_(0) - R`
`- k (l_(0) - R) + N = mR omega^(2)`
`N = mR omega^(2) + k (l_(0) - R)`
`f = mu N = mg`
`mu = (mg)/(N)`
`mu = (mg)/(mR omega^(2) + k (l_(0) - R))`