A) \[\frac{r}{2}\]
B) \[\frac{r}{\sqrt{2}}\]
C) \[\frac{r}{3}\]
D) \[\frac{r}{\sqrt{3}}\]
Correct Answer: D
Solution :
\[\frac{{{I}_{center}}}{{{I}_{edge}}}=\frac{{{({{r}^{2}}+{{h}^{2}})}^{3/2}}}{{{h}^{3}}}\] \[\Rightarrow 8=\frac{{{({{r}^{2}}+{{h}^{2}})}^{3/2}}}{{{h}^{3}}}\]\[\Rightarrow 2h={{({{r}^{2}}+{{h}^{2}})}^{1/2}}\] \[\Rightarrow 4{{h}^{2}}={{r}^{2}}+{{h}^{2}}\]\[\Rightarrow 3{{h}^{2}}={{r}^{2}}\]Þ \[h=\frac{r}{\sqrt{3}}\]
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