Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is $\sqrt{\frac{8}{x}}$. The value of x is: $\_\_\_\_$
Select the correct option:
A
37
B
17
C
67
D
51
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$\begin{aligned} & I_{\text {sphere }}=\frac{2}{3} M R^2=M k_1^2 \\ & I_{\text {cylinder }}=\frac{1}{12} M\left(4 R^2\right)+\frac{1}{4} M R^2+M(2 R)^2 \\ & =\frac{67}{12} M R^2=M k_2^2 \\ & \frac{k_1}{k_2}=\sqrt{\frac{2}{3} \cdot \frac{12}{67}}=\sqrt{\frac{8}{67}}\end{aligned}$
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