A long horizontal rod has a bead which can slide along its length, and initially it is at a distance L from the end A of the rod. The rod is set in angular motion about A with constant angular acceleration α in a gravity free space. If the coefficient of friction between the rod and the bead is μ , then the time after which the bead starts slipping is

Question

A long horizontal rod has a bead which can slide along its length, and initially it is at a distance L from the end A of the rod. The rod is set in angular motion about A with constant angular acceleration α in a gravity free space. If the coefficient of friction between the rod and the bead is μ , then the time after which the bead starts slipping is (A) √(μ /α ) (B) (μ/√α ) (C) (1/√μ α ) (D) infinitesimal

Tardigrade Admin · Accepted Answer

N=mα L When the bead starts slipping f max=μ N=mω 2L μ mα L=m(α t)2L ⇒ t=√(μ /α ) <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-dq0srmtrkwld.png" />

$\frac{μ}{α}$

$\frac{μ}{α}$

$\frac{1}{μα}$

infinitesimal

$N = m αL$
When the bead starts slipping
$f_{m a x} = μ N = m ω^{2} L$
$μ m αL = m (α t)^{2} L$
$\Rightarrow t = \frac{μ}{α}$

αμ​​

α​μ​

μα​1​

infinitesimal

N=mαL When the bead starts slipping fmax​=μN=mω2L μmαL=m(αt)2L ⇒t=αμ​​

$\frac{μ}{α}$

$\frac{μ}{α}$

$\frac{1}{μα}$

$N = m αL$
When the bead starts slipping
$f_{m a x} = μ N = m ω^{2} L$
$μ m αL = m (α t)^{2} L$
$\Rightarrow t = \frac{μ}{α}$