A uniform square plate of side a is suspended from a corner and executes small oscillations as a compound pendulum. Find its time period.
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Question

A uniform square plate of side a is suspended from a corner and executes small oscillations as a compound pendulum. Find its time period.

G1 Physics · Accepted Answer

For a square plate of side a pivoted at a corner, centre-of-mass distance h=a/√2. Moment of inertia about the corner is I=I about CM+Mh²=(Ma²/6)+(Ma²/2)=2Ma²/3. Hence T=2π√[I/(Mgh)]=2π√(√8 a/3g). Correct option: 1.