A uniform disc 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 $4 y = 3 x + c .$ Where c is constant. Find the value of $c (\tan 37^{o} = 0.75)$

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$\pm 20 c m$

$\pm 10 c m$

$\pm 8 c m$

$\pm 25 c m$

answer is C.

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Detailed Solution

$I_{Z} = \frac{M R^{2}}{2}$

The line, $4 y = 3 x + C o r y = \frac{3}{4} x + \frac{C}{4}$

$m = \tan θ = \frac{3}{4}; O B = \frac{C}{4}, θ = 37^{0}$

In $\begin{matrix} Δ O A B, O A = O B \cos 37^{0} = (\frac{C}{4}) (\frac{4}{5}) = \frac{C}{5} \\ I_{1} = I_{Z} = I_{O} + M {(\frac{c}{5})}^{2} [∵ P a r a l l e l a x e s t h e o r e m] \\ \frac{M R^{2}}{2} = \frac{M R^{2}}{4} + M {(\frac{c}{5})}^{2} \Rightarrow \frac{M R^{2}}{4} = M {(\frac{c}{5})}^{2} \Rightarrow \frac{C}{5} = \pm \frac{R}{2} \Rightarrow C = \pm \frac{5 R}{2} \end{matrix}$