A uniform circular disc of radius 'R' and mass 'M' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R/2 is removed from the original disc as shown in the figure. Find the moment of inerti

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Solution

Q.
A uniform circular disc of radius 'R' and mass 'M' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R/2 is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above. [2025]

1 $\frac{7}{32} M R^{2}$

2 $\frac{9}{32} M R^{2}$

3 $\frac{17}{32} M R^{2}$

4 $\frac{13}{32} M R^{2}$

Ans.
(4)

$I = I_{complete} - I_{removed}$

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

$I_{removed} = (\frac{M}{4}) {(\frac{R}{2})}^{2} \frac{1}{2} + (\frac{M}{4}) {(\frac{R}{2})}^{2} = \frac{3 M R^{2}}{32}$

$I = \frac{M R^{2}}{2} - \frac{3 M R^{2}}{32} = \frac{13}{32} M R^{2}$

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