A bead is constrained to move on rod in gravity free space as shown in figure. The rod is rotating with angular velocity $ω$ and angular acceleration $α$ about its end. If $μ$ is coefficient of friction. Mark the correct option. Rod rotates in the plane of paper.

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If bead does not slide relative to rod. Friction will not exist between rod and bead.

If $μ = \frac{ω^{2}}{α}$ friction on bead is astatic in nature.

If $μ > \frac{ω^{2}}{α}$ friction on bead is kinetic in nature.

If $μ < \frac{ω^{2}}{α}$ friction is static.

answer is A.

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Detailed Solution

$f = m L ω^{2} N = m L α$

If $μ = \frac{ω^{2}}{α} \Rightarrow μ N = m L ω^{2}$

if $μ > \frac{ω^{2}}{α} \Rightarrow f > m L ω^{2}, s o t h e b e a d w i l l b e a t r e s t (s t a t i c) μ < \frac{ω^{2}}{α} \Rightarrow f < m L ω^{2}, s o t h e b e a d w i l l n o t h a v e e n o u g h f r i c t i o n t o r o t a t e . I t w i l l s l i p (k i n e t i c)$