Question

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 $m$, and gravity is neglected, then the time after which the bead starts slipping is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Let the bead starts slipping after time $t$

For critical condition

Frictional force provides the centripetal force

$m{\omega }^{2}L=\mu R=\mu m\times a_t=\mu Lma$

$\Rightarrow m(at{)}^{2}L=\mu mLa\Rightarrow t=\sqrt{\frac{\mu }{a}}$ $(As\omega =at)$