A) \[{{\cot }^{-1}}\left( 1+\sqrt{\frac{2mg}{kh}} \right)\]
B) \[ta{{n}^{-1}}\left( 1+\sqrt{\frac{2mg}{kh}} \right)\]
C) \[{{\cot }^{-1}}\left( 1+\sqrt{\frac{mg}{kh}} \right)\]
D) \[ta{{n}^{-1}}\left( 1+\sqrt{\frac{mg}{kh}} \right)\]
Correct Answer: A
Solution :
[a] Loss in gravitational \[P.E.=\]gain in spring RE. \[mgh=\frac{1}{2}k{{\left( h\,cot\,\alpha \,-h \right)}^{2}}or\,\,\left( \cot \alpha -1 \right)=\sqrt{\frac{2mg}{kh}}\] Or, \[\cot \,\alpha =1+\sqrt{\frac{2mg}{kh}}\]
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