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Question

# Two balls each of mass 1 kg are connected to both ends of a uniform circular rod of mass 5 kg and length 2 m. 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
53 kg-m2
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B
2 kg-m2
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C
133 kg-m2
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D
113 kg-m2
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Solution

## The correct option is D 113 kg-m2Each ball of mass m=1 kg is at a distance of 1 m from axis OO' i.e d=1 m. So, moment of inertia of both balls is I1=2×md2=2×1×(1)2 I1=2 kg-m2...(I) Moment of inertia of uniform circular rod of mass M=5 kg and length l=2 m about OO' is I2=Ml212=5×(2)212=53 kg-m2 ...(II) So, Moment of inertia of system about axis OO' : I=I1+I2 =2+53=113 kg-m2

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