A) \[\frac{4}{3}R\]
B) \[\frac{\sqrt{17}}{2}R\]
C) \[\sqrt{13}R\]
D) \[\frac{\sqrt{15}}{2}R\]
Correct Answer: B
Solution :
An axis passing through \[x\,=\,2R\], \[y\,=\,0\] is in direction as shown in figure. Moment of inertia about this axis will be: |
\[{{l}_{1}}=\frac{1}{2}m{{R}^{2}}+m{{\left( 2R \right)}^{2}}=\frac{9}{2}m{{R}^{2}}\] ...(1) |
Axis passing through \[y=d,z=0\]is shown as dotted line in figure. Moment of inertia about this axis will be: |
\[{{l}_{2}}=\frac{1}{4}m{{R}^{2}}+m{{d}^{2}}\] ...(2) |
Eqs. (1) and (2), we get, \[\frac{1}{4}m{{R}^{2}}+m{{d}^{2}}=\frac{9}{2}m{{R}^{2}}\] or \[d=\frac{\sqrt{17}}{2}R\] |
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