A) \[{{\rho }_{1}}{{\rho }_{2}}:1\]
B) \[1:{{\rho }_{1}}{{\rho }_{2}}\]
C) \[{{\rho }_{1}}:{{\rho }_{2}}\]
D) \[{{\rho }_{2}}:{{\rho }_{1}}\]
Correct Answer: D
Solution :
From the formula, \[{{I}_{1}}=\frac{1}{2}m{{r}^{2}}\] and \[{{I}_{2}}=\frac{1}{2}mr_{2}^{2}\] Then, \[\frac{{{I}_{1}}}{{{I}_{2}}}=\frac{\frac{1}{2}mr_{1}^{2}}{\frac{1}{2}mr_{2}^{2}}=\frac{r_{1}^{2}}{r_{2}^{2}}\] If t is thickness of each plate, then \[\pi r_{1}^{2}t{{\rho }_{1}}=\pi r_{2}^{2}{{\rho }_{2}}\] or \[\frac{r_{1}^{2}}{r_{2}^{2}}=\frac{{{\rho }_{2}}}{{{\rho }_{1}}}\] \[\therefore \] \[\frac{{{I}_{1}}}{{{I}_{2}}}=\frac{r_{1}^{2}}{r_{2}^{2}}=\frac{{{\rho }_{2}}}{{{\rho }_{1}}}\]
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