A) 4 rad/s
B) 16 rad/s
C) \[\sqrt{21}\]rad/s
D) 2 rad/s
Correct Answer: A
Solution :
Key Idea: Tension in thread in vertical circular motion is maximum at the lowest point. At the lowest point of vertical circular motion \[{{T}_{\max }}=mg+\frac{m{{v}^{2}}}{r}\] or \[{{T}_{\max }}=mg+mr{{\omega }^{2}}\] ?(i) Given, \[{{T}_{\max }}=3.7\times 10=37N\] \[mg=0.5\times 10-5N\] Thus, Eq.(i), becomes \[37=5+0.5\times 4\times {{\omega }^{2}}\] or \[{{\omega }^{2}}=\frac{37-5}{0.5\times 4}=\frac{32}{2}=16\] or \[\omega =4\,rad/s\]
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