A cylindrical block of density d stays fully immersed in a beaker filled with two immiscible liquids of different densities d 1 and d 2 . The block is in equilibrium with half of it in liquid 1 an

Question

A cylindrical block of density d stays fully immersed in a beaker filled with two immiscible liquids of different densities d 1 ​ and d 2 ​ . The block is in equilibrium with half of it in liquid 1 and the other half in liquid 2 (Figure 5.144). If the block is given a displacement downwards and released, then, neglecting frictional losses:

TestHub · Accepted Answer

Displacing the block by x replaces liquid 1 by liquid 2 over length x , giving restoring force A g ( d 2 ​ − d 1 ​ ) x , proportional to x . Mass = A h d , so ω 2 = h d g ( d 2 ​ − d 1 ​ ) ​ depends on the height h . The motion is symmetric about equilibrium while the block stays across the interface.

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