A) 1 : 32
B) 1 : 16
C) 1 : 8
D) 1 : 4
Correct Answer: A
Solution :
From the formula the moment of inertia of sphere is \[I=\frac{2}{5}m{{r}^{2}}\] where \[m=\frac{4}{3}\pi {{r}^{3}}\rho \] where \[\rho \] is the density of the body so, \[I=\frac{2{{r}^{2}}}{5}\times \frac{4}{3}\pi {{r}^{3}}\rho =\frac{8}{15}\pi \rho {{r}^{3}}\] \[I\propto {{r}^{5}}\] Therefore, moment of inertia is proportional to\[{{r}^{5}}\]. Hence ratio will be\[1:{{2}^{5}}=1:32.\]
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