A) 3 : 1
B) 3 : 2
C) \[\sqrt{3}:1\]
D) \[2\sqrt{3}:1\]
Correct Answer: D
Solution :
\[\frac{{{M}_{1}}}{{{M}_{2}}}=\frac{\tan {{\theta }_{1}}}{\tan {{\theta }_{2}}}\Rightarrow \frac{{{m}_{1}}{{L}_{1}}}{{{m}_{2}}{{L}_{2}}}=\frac{\tan {{\theta }_{1}}}{\tan {{\theta }_{2}}}\] \[\Rightarrow \frac{{{m}_{1}}}{{{m}_{2}}}=\frac{2}{1}\times \frac{\tan 45{}^\circ }{\tan 30{}^\circ }=\frac{2\sqrt{3}}{1}\]
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