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$ \alpha $ . If the coefficient of friction between the rod and the bead is $ \mu $ , and gravity is neglected, then the time after which the bead starts slipping is
Options:
A) $ \sqrt{\frac{\mu }{\alpha }} $
B) $ \frac{\mu }{\sqrt{\alpha }} $
C) $ \frac{1}{\sqrt{\mu \alpha }} $
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{{\omega }^{2}}L=\mu R=\mu m\times a _{t}=\mu Lm\alpha $ $ \Rightarrow m{{\omega }^{2}}L=\mu R=\mu m\times a _{t}=\mu Lm\alpha $
$ \Rightarrow m{{(\alpha t)}^{2}}L=\mu mL\alpha t=\sqrt{\frac{\mu }{\alpha }} $
