A) \[\frac{3M{{R}^{2}}}{32}\]
B) \[\frac{5M{{R}^{2}}}{16}\]
C) \[\frac{11M{{R}^{2}}}{64}\]
D) none of these
Correct Answer: C
Solution :
Mass of cut disc: \[{{m}_{1}} = M/4\] Moment of Inertia of original disc about axis 1: \[I=\frac{1}{4}\,M{{R}^{2}}\] Moment of Inertia of small disc about axis 1: \[I'=\frac{1}{4}{{m}_{1}}\,{{\left( \frac{R}{2} \right)}^{2}}\,\,+{{m}_{1}}\,{{\left( \frac{R}{2} \right)}^{2}}\,\,\,\,\,\,\,\,[Parallel\,\,axis\,\,theorem]\]\[\frac{5}{16}\,{{m}_{1}}{{R}^{2}}\,\,=\,\,\,\frac{5}{64}M{{R}^{2}}\] Required moment of inertia: \[I-I'=\frac{1}{4}\,M{{R}^{2}}\,-\,\,\frac{5}{64}M{{R}^{2}}\,=\,\frac{11}{64}\,\,M{{R}^{2}}\]You need to login to perform this action.
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