Fluid Mechanics

JEE Main level, single correct, medium

33 of 192

Question 33 of 192

A cubical block of density ρb=600 kg/m3\rho_{b}=600 \mathrm{~kg} / \mathrm{m}^{3} floats in a liquid of density ρe=900kg/m3\rho_{\mathrm{e}}=900 \mathrm{kg} / \mathrm{m}^{3}. If the height of block is H=8.0 cmH=8.0 \mathrm{~cm} then height of the submerged part is ____\_\_\_\_ cm.

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Answer: (C) 5.3

For a floating cubical block in equilibrium, the buoyant force equals the weight:
ρe⋅g⋅A⋅hs=ρb⋅g⋅A⋅H\rho_e \cdot g \cdot A \cdot h_s = \rho_b \cdot g \cdot A \cdot H
where hsh_s is the submerged height.
Simplifying: hs=ρbρe⋅H=600900×8.0=23×8.0h_s = \frac{\rho_b}{\rho_e} \cdot H = \frac{600}{900} \times 8.0 = \frac{2}{3} \times 8.0
=5.33= 5.33 cm ≈ 5.3 cm

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