SATHEE: Laws Of Motion Question 152

Laws Of Motion Question 152

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 $α$ . If the coefficient of friction between the rod and the bead is $μ$ , and gravity is neglected, then the time after which the bead starts slipping is

Options:

A) $\sqrt{\frac{μ}{α}}$

B) $\frac{μ}{\sqrt{α}}$

C) $\frac{1}{\sqrt{μ α}}$

D) Infinitesimal

Show Answer

Answer:

Correct Answer: A

Solution:

[a] Let the bead starts slipping after time t. for critical condition frictional force provides the centripetal force $m ω^{2} L = μ R = μ m \times a_{t} = μ L m α$ $\Rightarrow m ω^{2} L = μ R = μ m \times a_{t} = μ L m α$

$\Rightarrow m {(α t)}^{2} L = μ m L α t = \sqrt{\frac{μ}{α}}$

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Laws Of Motion Question 152

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