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Q108 (CGS/2026) Science & Technology › Basic Science (Physics, Chemistry, Biology)

A block of wood floats in water with 3⁄4th of its volume submerged. The same block floats in another fluid with 2⁄3rd of its volume submerged. What is the specific gravity of the fluid?

Result
Your answer: —  ·  Correct: C

Explanation

According to the Law of Flotation, the weight of a floating body is equal to the weight of the liquid displaced by its submerged part. This is expressed as:
ρbody × Vtotal = ρliquid × Vsubmerged

Let V be the total volume of the wood block. For the block floating in water:
ρwood × V = ρwater × (3/4)V
ρwood = (3/4)ρwater

For the same block floating in the other fluid:
ρwood × V = ρfluid × (2/3)V
ρwood = (2/3)ρfluid

Equating the two expressions for ρwood:
(3/4)ρwater = (2/3)ρfluid

The specific gravity of the fluid is the ratio of its density to the density of water:
Specific Gravity = ρfluid / ρwater = (3/4) ÷ (2/3) = (3/4) × (3/2) = 9/8

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