The time period of a bar pendulum when suspended at distances 30 cm and 50 cm from its centre of gravity comes out to be the same. If the mass of the body is 2 kg. Find out its moment of inertia about an axis passing through first point.
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Question

The time period of a bar pendulum when suspended at distances 30 cm and 50 cm from its centre of gravity comes out to be the same. If the mass of the body is 2 kg. Find out its moment of inertia about an axis passing through first point.

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G1 Physics · Accepted Answer

For a physical pendulum, equal periods at h₁=0.30 m and h₂=0.50 m imply radius-of-gyration²=h₁h₂=0.15 m², so I about CM=Mradius-of-gyration²=2×0.15=0.30 kg m². About the first suspension point, I=I about CM+Mh₁²=0.30+2(0.09)=0.48 kg m². Correct answer: C.