A) \[{{I}_{A}}>{{I}_{B}}\]
B) \[{{I}_{A}}={{I}_{B}}\]
C) \[{{I}_{A}}<{{I}_{B}}\]
D) depends on the actual value of t and r
Correct Answer: C
Solution :
[c] Since moment of inertia \[I=\frac{m{{r}^{2}}}{2}\], where m is the mass of body & r is distance of it from the fixed axis. mass = density \[\times \] volume \[\{\therefore \rho =\,density\}\] \[{{M}_{A}}=\rho \pi \,{{r}^{2}}t;\]\[{{I}_{A}}=\frac{\rho \pi {{r}^{4}}t}{2}\] \[{{M}_{B}}=\rho \pi \,{{r}^{2}}\times 16\times t/4=4\rho \pi {{r}^{2}}t\] \[{{I}_{B}}=\frac{M{{\,}_{B}}{{(4r)}^{2}}}{2}=\frac{4\rho \pi {{r}^{2}}t.16{{r}^{2}}}{2}\] \[=\frac{64\rho \pi {{r}^{4}}t}{2}\] \[\therefore \]\[{{I}_{B}}>{{I}_{A}}\]
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