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Two circular loops of radii R and nR are made of same wire. If their M.I about their normal axis through centre are in the ratio $1 : 8$ , the value of n is

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answer is C.

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Detailed Solution

\frac{I_{1}}{I_{2}} = \frac{1}{8}

$λ = \frac{m}{l}$

$m = λ l$

$m_{1} = λ \times 2 π R_{1}$

$m_{2} = λ (2 π R_{1}) n$

$\frac{m_{1} R_{1}^{2}}{m_{2} R_{2}^{2}} = \frac{1}{8}$

$\frac{λ \times 2 π R \times R^{2}}{λ \times 2 π R \times n \times n^{2} R^{2}} = \frac{1}{8}$

$\frac{1}{n^{3}} = \frac{1}{2^{3}}$

$n = 2$

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