A) \[\frac{1}{4}M{{r}^{2}}\]
B) \[\frac{2}{5}M{{r}^{2}}\]
C) \[M{{r}^{2}}\]
D) \[\frac{1}{2}M{{r}^{2}}\]
Correct Answer: D
Solution :
| [d] The mass of complete (circular) disc is |
 |
 |
| The moment of inertia of disc about the given axis is |
| \[l=\frac{2M{{r}^{2}}}{2}=M{{r}^{2}}\] |
| The disc may be assumed as combination of two semi-circular parts. |
| Thus, the moment of inertia of a semi-circular part of disc, |
| \[{{l}_{1}}-l-{{l}_{1}}\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,{{l}_{1}}=\frac{l}{2}=\frac{M{{r}^{2}}}{2}\] |
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