A) \[{{I}_{Y}}=64{{I}_{X}}\]
B) \[{{I}_{Y}}=32{{I}_{X}}\]
C) \[{{I}_{Y}}=16{{I}_{X}}\]
D) \[{{I}_{Y}}={{I}_{X}}\]
Correct Answer: A
Solution :
[a] Moment of Inertia of disc \[I=\frac{1}{2}M{{R}^{2}}\] \[=\frac{1}{2}(\pi {{R}^{2}}t\rho ){{R}^{2}}=\frac{1}{2}\pi t\rho {{R}^{4}}\] \[As\,\,M=V\times \rho =\pi {{R}^{2}}t\rho \,\,where\,\,t=thickness,\,\,\rho =density]\] \[\therefore \frac{{{I}_{y}}}{{{I}_{x}}}=\frac{{{t}_{y}}}{{{t}_{x}}}{{\left( \frac{{{R}_{y}}}{{{R}_{x}}} \right)}^{4}}[if\,\,\rho =constant]\] \[\Rightarrow \frac{{{I}_{y}}}{{{I}_{x}}}=\frac{1}{4}{{(4)}^{4}}=64[Given\text{ }{{R}_{y}}=4{{R}_{x}},\,\,\,{{t}_{y}}=\frac{{{t}_{x}}}{4}]\] \[\Rightarrow {{I}_{y}}=64{{I}_{x}}\]
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