A cubical block of density b = 600 kg/m^3 floats in a liquid of density l = 900 kg/m^3. If the height of block is H = 8.0 cm, then height of the submerged part is cm.

Given: A cubical block has density b = 600 kg/m^3, the liquid has density l = 900 kg/m^3, and the block height is H = 8.0 cm. Find: The height h of the submerged part. For a floating body, Volume submerged Total volume = b l Since the block is cubical, the fraction of submerged volume equals the fraction of submerged height: hH = 600900 = 23 Therefore, h = 23 8 = 163 5.3 cm Therefore, the height of the submerged part is 5.3 cm. The correct option is A.

A cubical block of density b = 600 kg/m^3 floats in a liquid of d… — Solution | JEE Physics

MCQEasyJEE 2026Fluid Pressure & Pascal's Law

A cubical block of density $\rho_b = 600\,kg/m^3$ floats in a liquid of density $\rho_l = 900\,kg/m^3$ . If the height of block is $H = 8.0\,cm$ , then height of the submerged part is _____ cm.

A
$5.3$
B
$6.3$
C
$7.3$
D
$4.3$

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: A cubical block has density $\rho_b = 600\,kg/m^3$ , the liquid has density $\rho_l = 900\,kg/m^3$ , and the block height is $H = 8.0\,cm$ .

Find: The height $h$ of the submerged part.

For a floating body,

\frac{\text{Volume submerged}}{\text{Total volume}} = \frac{\rho_b}{\rho_l}

Since the block is cubical, the fraction of submerged volume equals the fraction of submerged height:

\frac{h}{H} = \frac{600}{900} = \frac{2}{3}

Therefore,

h = \frac{2}{3} \times 8 = \frac{16}{3} \approx 5.3\,\text{cm}

Therefore, the height of the submerged part is $5.3\,\text{cm}$ . The correct option is A.

Common mistakes

Using the ratio $\frac{\rho_l}{\rho_b}$ instead of $\frac{\rho_b}{\rho_l}$ . This is wrong because the submerged fraction of a floating body equals body density divided by liquid density. Use $\frac{h}{H} = \frac{\rho_b}{\rho_l}$ .
Treating the block as if full volume is submerged. This is wrong because a floating body displaces only enough liquid to balance its weight. First find the submerged fraction, then multiply by the total height.

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