A liquid of density 2p is filled in a cylindrical area is 2A. A wooden cylinder of height H, cross-sectional area A and density p is floating in the liquid at equilibrium with its axis vertical. The cylinder is pushed down by a small distance x from its equilibrium position and released. Find its initial acceleration.
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Given A liquid of density 2p is filled in a cylindrical area is 2A. A wooden cylinder of height H, cross-sectional area A and density p is floating in the liquid at equilibrium with its axis vertical. The cylinder is pushed down by a small distance x from its equilibrium position and released. Find its initial acceleration.
- The volume of the part of cylinder under the initial water level after displacement is increased by
- So ΔV = A x x
- Now water level rises so
- So x water = ΔV / 2A – A = x
- Now total volume under water is 2Ax. The force upward from Archimedes principle is
- F = ρ water g(2 Ax)
- Now acceleration will be a = ρ water g(2 Ax) / m
- = 2 pg 2 Ax / p AH
= 4 g x / H
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