A) \[(3/4)m{{l}^{2}}\]
B) \[2\,m{{l}^{2}}\]
C) \[(5/4)\,\,m{{l}^{2}}\]
D) \[(3/2)\,\,m{{l}^{2}}\]
Correct Answer: C
Solution :
Moment of inertia of the system about AX is given by \[MI={{m}_{A}}r_{A}^{2}+{{m}_{B}}r_{B}^{2}+{{m}_{C}}r_{C}^{2}\] \[MI=m{{(0)}^{2}}+m{{(l)}^{2}}+m{{(l\sin {{30}^{0}})}^{2}}\] \[=m{{l}^{2}}+\frac{m{{l}^{2}}}{4}=\frac{5}{4}m{{l}^{2}}\] Alternative: Moment of inertia of a system about a line OC perpendicular to AB, in the plane of ABC is \[{{I}_{CO}}=m\times 0+m\times {{\left( \frac{1}{2} \right)}^{2}}+m\times {{\left( \frac{1}{2} \right)}^{2}}\] \[\therefore \]\[{{I}_{CO}}=\frac{m{{l}^{2}}}{4}+\frac{m{{l}^{2}}}{4}=\frac{m{{l}^{2}}}{2}\] According to parallel-axis theorem \[{{I}_{AX}}={{I}_{CO}}+M{{x}^{2}}\] where\[x=\] distance of \[AX\] from CO, \[M=\] total mass of system \[{{I}_{AX}}=\frac{m{{l}^{2}}}{2}+3m\times {{\left( \frac{l}{2} \right)}^{2}}\] \[{{I}_{AX}}=\frac{m{{l}^{2}}}{2}+\frac{3m{{l}^{2}}}{4}=\frac{5}{4}m{{l}^{2}}\]You need to login to perform this action.
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