A long horizontal rod has a bead which can slide along its length, and initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with constant angular acceleration a . If the coefficient of friction between the rod and the bead is m μ , and gravity is neglected, then the time after which the bead starts slipping is
Text Solution
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Let the bead starts slipping after time t
For critical condition
Frictional force provides the centripetal force
\(m \dot{z}^2 L = \mu R = \mu m > a = \mu L m <\)
⇒ ⇒ m(x,a)^2 l = g m l x ⇒ ⇒ \(\varepsilon \sqrt{\frac{k}{\mu}}\) (As r^v = r^t )
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