Double the Trouble

Classical Mechanics Level 3

A cubical wooden block floats at the interface between oil and water with 2 c m 2 cm of its length below water and 8 c m 8 cm above it, as shown. If the density of the oil is 0.6 g / c m 3 0.6 g/{ cm }^{ 3 } , determine the relative density of the block.


The answer is 0.68.

Rishav Koirala by Rishav Koirala , 22, Singapore

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2 solutions

Himanshu Arora
May 30, 2014

Apply the Archimedes' Principle , the weight of the fluids displaced would be proportional to the height immersed in it. So, d × 10 = 1 × 2 + 0.6 × 8 d\times 10 = 1\times 2 + 0.6\times 8 . Hence the answer d = 0.68 d= \boxed{0.68}

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if we consider the block of wood, the weight of the block is acting downwards, buoyant forces of water and oil are trying to push it upwards. Foil +Fwater = W the buoyant force is equal to the weight of the fluid displaced taking unit area, density(oil) 8 g + density(water) 2 g = density of block (8+2) g ie.

(0.6x8) +(1x2) = 10*relative density of block

from above eqn relative density = .68

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