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PhysicsFluidArchimedes principleMedium3 minQB

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Passage / Comprehension

Two ice cubes each have side 10 cm and a central cavity of volume $20 cm^{3}$ . The cavities contain materials A and B, of specific gravity 4.9 and 1.9 respectively.
They are placed in separate vessels of equal base area with equal initial water level. The ice melts uniformly from every side at the same constant rate. Specific gravity of ice is 0.9.

Find the ratio of initial submerged volumes of the blocks containg A and B respectively

Options:

Answer:

Solution:

The cube volume is 1000 cm³, with 20 cm³ of filling and 980 cm³ of ice.
For each floating block, the displaced water weighs as much as the block.
$v_{A} ρ_{w} = (1000 - 20) ρ_{i} + 20 ρ_{A}$
$v_{B} ρ_{w} = (1000 - 20) ρ_{i} + 20 ρ_{B}$
$\frac{v _{A}}{v _{B}} = \frac{980 ( 0.9 ) + 20 ( 4.9 )}{980 ( 0.9 ) + 20 ( 1.9 )}$
$\frac{v _{A}}{v _{B}} = \frac{49}{46}$
Option A.

Stream:JEESubject:PhysicsTopic:FluidSubtopic:Archimedes principle

⏱ 3mℹ️ Source: QB

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