A) \[\frac{7}{12}m{{L}^{2}}\]
B) \[\frac{11}{14}m{{L}^{2}}\]
C) \[\frac{5}{15}m{{L}^{2}}\]
D) \[\frac{11}{12}m{{L}^{2}}\]
Correct Answer: D
Solution :
[d] The moment of the rod on the y axis about the y axis itself is essentially zero (axis through axis centre,' parallel to rod) because the rod is thin. The moments of the rods on the x and z axes are each \[I=\frac{1}{12}M{{L}^{2}}\] (Axis through centre, perpendicular to rod) from the table in the chapter. The total moment of the three rods about the axis (and about the CM) is \[{{I}_{CM}}={{I}_{on\,x\,axis}}+{{I}_{on\,y\,axis}}+{{I}_{on\,z\,axis}}\] \[=\frac{1}{12}M{{L}^{2}}+0+\frac{1}{12}M{{L}^{2}}=\frac{1}{2}m{{L}^{2}}\] For the moment of the rod-combination about the axis of rotation, the parallel-axis theorem gives \[I={{I}_{CM}}+3m{{\left( \frac{L}{2} \right)}^{2}}=\left[ \frac{1}{6}+\frac{3}{4} \right]m{{L}^{2}}\] \[=\left[ \frac{2}{12}+\frac{9}{12} \right]m{{L}^{2}}=\frac{11}{12}m{{L}^{2}}\]You need to login to perform this action.
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