A thin cylindrical rod PQ of length L and density d 1 is pivoted at its lowest point P, inside a stationary homogeneous and non- viscous liquid of density d 2 . The rod is always fully submerged inside the liquid and is free to rotate in a vertical plane about a horizontal axis passing through P. If d 1 < d 2 , then the time period of small angular oscillations of the rod about its vertical equilibrium position will be
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Consider the diagram in a displaced position.
The weight and upthrust F b , both pass through the center of gravity G
W = ( 
r 2 L) d 1 g
F B = ( 
r 2 L) d 2 g
The restoring torque about the pivot is
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