Question:
A cubical block of density \( \rho_b = 600\,\text{kg/m}^3 \) floats in a liquid of density \( \rho_l = 900\,\text{kg/m}^3 \). If the height of block is \(H = 8.0\,\text{cm}\), then height of the submerged part is ________ cm.
A cubical block of density \( \rho_b = 600\,\text{kg/m}^3 \) floats in a liquid of density \( \rho_l = 900\,\text{kg/m}^3 \). If the height of block is \(H = 8.0\,\text{cm}\), then height of the submerged part is ________ cm.
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Fraction submerged of a floating body depends only on density ratio.
Updated On: Feb 5, 2026
- 5.3
- 6.3
- 7.3
- 4.3
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The Correct Option is A
Solution and Explanation
Step 1: Apply floating condition.
For a floating body, \[ \frac{\text{Volume submerged}}{\text{Total volume}} = \frac{\rho_b}{\rho_l} \]
Step 2: Substitute given values.
\[ \frac{h}{H} = \frac{600}{900} = \frac{2}{3} \]
Step 3: Calculate submerged height.
\[ h = \frac{2}{3} \times 8 = \frac{16}{3} \approx 5.3\,\text{cm} \]
For a floating body, \[ \frac{\text{Volume submerged}}{\text{Total volume}} = \frac{\rho_b}{\rho_l} \]
Step 2: Substitute given values.
\[ \frac{h}{H} = \frac{600}{900} = \frac{2}{3} \]
Step 3: Calculate submerged height.
\[ h = \frac{2}{3} \times 8 = \frac{16}{3} \approx 5.3\,\text{cm} \]
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