A) \[\frac{M{{\omega }^{2}}L}{M{{\omega }^{2}}-k}\]
B) \[\frac{M{{\omega }^{2}}L}{k-M\,{{\omega }^{2}}}\]
C) \[\frac{M{{\omega }^{2}}}{k}\]
D) \[\frac{kL}{M{{\omega }^{2}}}\]
Correct Answer: B
Solution :
Let AL be increase in length of spring. Particle will move on a circular path of radius\[\left( L + \Delta L \right)\]. Restoring force due to spring \[=\,\,k\,\Delta L\] By force balance \[\operatorname{M}{{\omega }^{2}}(L +\,\,\Delta L) =\,\,k\Delta L\,\,\,\Rightarrow \,\,\Delta L = \,\frac{M\,{{\omega }^{2}}\cdot L}{k-M\,{{\omega }^{2}}}\]
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