A) 1 cm
B) 2 cm
C) 4 cm
D) 8 cm
Correct Answer: A
Solution :
The object will slip if centripetal force \[\le \]force of friction i.e., \[\frac{m{{v}^{2}}}{r}\ge \mu R\] \[m{{\omega }^{2}}r\ge \mu mg\] \[(\because v=r\omega ,R=mg)\] \[{{\omega }^{2}}r\ge \mu g\] \[r\propto \frac{1}{{{\omega }^{2}}}\] \[\frac{{{r}_{2}}}{{{r}_{1}}}={{\left( \frac{{{\omega }_{1}}}{{{\omega }_{2}}} \right)}^{2}}\] Put \[{{r}_{1}}=4\,cm,{{\omega }_{2}},{{\omega }_{2}}=2\omega \]
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