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A uniform dise of radius 8cm lies in the x-y plane, with its centre at origin. Its moment of inertia about z-axis is equal to its moment of inertia about the line $4 y = 3 x + 4 c$ . Where c is constant. Find the value of $c (\tan 37^{\circ} = 0 .75)$

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$\pm 2 cm$

$\pm 4 cm$

$\pm 5 cm$

$\pm 8 cm$

answer is C.

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Detailed Solution

Given $I_{2} = I_{1}$

$\frac{{MR}^{2}}{4} + M \cdot {[\frac{4 C}{5}]}^{2} = \frac{{MR}^{2}}{2}$

$\Rightarrow \frac{16 C^{2}}{25} = \frac{R^{2}}{4} \Rightarrow \frac{16 C^{2}}{25} = \frac{(8)^{2}}{4}$

$∴ c = \pm 5 cm$

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