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: Condition of floating body.
For a floating body, weight of the object is equal to the buoyant force:
\[ Mg = F_b \]
Step 2: Expressing weight and buoyant force.
\[ \rho_{\text{object}} A H g = \rho_{\text{liquid}} A h g \]
where $H$ is total height and $h$ is submerged height.
Step 3: Substituting given values.
\[ 600 \times 8 = 900 \times h \]
Step 4: Solving for submerged height.
\[ h = \dfrac{600 \times 8}{900} = \dfrac{16}{3}\,\text{cm} \]