Let the moment of inertia of a hollow cylinder of length 30 cm [inner radius 5 cm and outer radius 10 cm] about its axis be I. The radius of a thin cylinder of the same mass and length such that its moment of inertia about its axis is also , is approximately.

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12 cm

18 cm

16 cm

8 cm

answer is C.

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Detailed Solution

$I_{t h i n} = m k^{2} \begin{array}{l} I_{h o l l o w} = \frac{m}{2} [{(5)}^{2} + {(10)}^{2}] \\ A s, I_{t h i n} = I_{h o l l o w} \Rightarrow K = \sqrt{\frac{{(5)}^{2} + {(10)}^{2}}{2}} = \sqrt{\frac{125}{2}} \\ = 7.9 c m \\ ≃ 8 (a p p r o x) \end{array}$

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