Question

3. A body of volume 36 cm floats with 3/4
of its volume submerged in water. The
density of water will be
.B
(a) 1 g/cm (b) 0.9 g/cm
(c) 0.75 g/cm3 (d) 0.25 g/cm​

Answer 1

Given:

• Volume of body = 36 cm³
• It floats in water with ¾ th volume inside.

To find:

• Density of the solid ?

Calculation:

Since the body is floating, the weight of the body is equal and opposite to the buoyant force exerted by water.

$f_{weight} = f_{buoyant}$

$\implies \: mg = V_{in}( \rho \times g)$

$\implies \: V_{total}( \sigma) g = V_{in}( \rho \times g)$

• $\sigma$ is density of body and $\rho$ is density of water.

$\implies \: V_{total} \times \sigma= V_{in} \times \rho$

$\implies \: \sigma= \dfrac{V_{in}}{ V_{total} } \times \rho$

$\implies \: \sigma= \dfrac{3}{ 4} \times 1$

$\implies \: \sigma= \dfrac{3}{ 4}$

$\implies \: \sigma= 0.75 \: g/cc$

So, density of body is 0.75 g/cc (option c)