Question

As shown in figure, $A$ rod $AB$ $\left(l_{AB}=2m\right)$ is hinged at point $A$ and its other end $B$ attached to a platform on which a block of mass $m$ is kept. The platform is not frictionless. Rod rotates about point $A$ maintaining angle $\theta =30^o$ with the vertical in such a way that platform remains horizontal and revolves on the horizontal circular path. What is the maximum angular velocity in $rad{s}^{-1}$ of rod so that the block does not slip on the platform? $\left(g=10m{s}^{-2},\mu =0.1\right)$

Answer 1

Answer: 1

$N=mg,\mu N=mr{\omega }^2$
$r=2sin\theta$
$\mu mg=m\left(2sin\theta \right){\left(\omega \right)}^2$
$\Rightarrow \omega =\sqrt{\frac{\mu \theta }{2sin\theta }}=\sqrt{\frac{0.1\times 10}{2\times sin20}}=1rad{s}^{-1}$