A) \[2\text{ }rad\,{{s}^{-1}}\]
B) \[4\,rad\,{{s}^{-1}}\]
C) \[8\,rad\,{{s}^{-1}}\]
D) \[16\,rad\,{{s}^{-1}}\]
Correct Answer: B
Solution :
Maximum tension in the thread is given by \[{{T}_{\max }}=mg+\frac{m{{v}^{2}}}{r}\] or \[{{T}_{\max }}=mg+mr{{\omega }^{2}}\] \[(\because \,v=r\omega )\] or \[{{\omega }^{2}}=\frac{{{T}_{\max }}-mg}{mr}\] Given, \[{{T}_{\max }}=37\,N,\,m=500g=0.5\,kg,\,g=10\,m{{s}^{-2}},\] \[r=4\,m\] \[\therefore \] \[{{\omega }^{2}}=\frac{37-0.5\times 10}{0.5\times 4}=\frac{37-5}{2}\] or \[{{\omega }^{2}}=16\] or \[\omega =4\,rad\,{{s}^{-1}}\]
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