Question

A cylindrical object of density $600\,\text{kg/m}^3$ and height $8$ cm is floating in a liquid of density $900\,\text{kg/m}^3$. Find height of cylinder inside liquid.

• A. $\dfrac{16}{3}$ cm
• B. $\dfrac{20}{3}$ cm
• C. $\dfrac{5}{3}$ cm
• D. $\dfrac{25}{3}$ cm

Hint:

For floating bodies, the fraction submerged depends only on the ratio of densities, not on mass or shape.

Answer 1

The Correct Option is A

Step 1: Use density ratio principle for floating bodies

For a body floating in a liquid, the fraction of volume submerged is equal to the ratio of the density of the object to the density of the liquid.

Submerged fraction = ρ_object / ρ_liquid

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Step 2: Apply the relation to the given body

ρ_object = 600 kg/m³
ρ_liquid = 900 kg/m³

Submerged fraction = 600 / 900 = 2 / 3

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Step 3: Calculate submerged height

Total height of the body, H = 8 cm

Submerged height,
h = (2 / 3) × 8

h = 16 / 3 cm

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Final Answer:

The height of the body submerged in the liquid is
h = 16 / 3 cm