A uniform rod of length L is used as a compound pendulum. Find the minimum possible period and the corresponding distance of the point of suspension from its centre.
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Question

A uniform rod of length L is used as a compound pendulum. Find the minimum possible period and the corresponding distance of the point of suspension from its centre.

G1 Physics · Accepted Answer

For a uniform rod, I about a point distance h from its centre is M(L²/12+h²). Equivalent length is Lₑ=I/(Mh)=L²/(12h)+h. Minimize: dLₑ/dh=−L²/(12h²)+1=0, giving h=L/(2√3). Then Lₑ=L/√3 and Tₘᵢₙ=2π√[L/(√3g)]. Correct option: 1.