Two balls each of mass 1kg are connected to both ends of a uniform circular rod of mass 5kg and length 2m. Find the moment of inertia of the system about an axis passing through the middle of the rod and perpendicular to the length of the rod.
A
53kg-m2
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B
2kg-m2
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C
133kg-m2
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D
113kg-m2
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Solution
The correct option is D113kg-m2 Each ball of mass m=1kg is at a distance of 1m from axis OO' i.e d=1m. So, moment of inertia of both balls is I1=2×md2=2×1×(1)2 I1=2kg-m2...(I)
Moment of inertia of uniform circular rod of mass M=5kg and length l=2m about OO' is I2=Ml212=5×(2)212=53kg-m2 ...(II) So, Moment of inertia of system about axis OO' : I=I1+I2 =2+53=113kg-m2