A rectangular block of height and density floats at the interface between two…

PHYSICS · Single correct · AP · Physics 1: Algebra-based · Fluids · Fluids

Problem

A rectangular block of height 10 cm10\,\text{cm} and density 950 kg m−3950\,\text{kg m}^{-3} floats at the interface between two immiscible liquids. Initially the upper liquid has density 800 kg m−3800\,\text{kg m}^{-3} and the lower liquid has density 1000 kg m−31000\,\text{kg m}^{-3}. At this stage, 2.5 cm2.5\,\text{cm} of the block is in the upper liquid and the rest in the lower liquid. The upper liquid is now carefully replaced by a different immiscible liquid of density 600 kg m−3600\,\text{kg m}^{-3}, the lower liquid remaining the same. After a new equilibrium is reached, how much of the block’s height will be immersed in the lower liquid? (a) 9.5 cm9.5\,\text{cm} (b) 8.75 cm8.75\,\text{cm} (c) 7.5 cm7.5\,\text{cm} (d) 8.0 cm8.0\,\text{cm}

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