Question

an ice cube floats in a liquid with 25% of its volume above the liquid surface if the density of ice is given as 930 kg m^3 then the density of the liquid is _____ g cm^3 ​

Answer 1

Given:

An ice cube floats in a liquid with 25% of its volume above the liquid surface ; the density of ice is given as 930 kg/m³.

To find:

Density of liquid (in g/cm³) ?

Calculation:

As per condition of floating , the weight of the ice is equal and opposite to the buoyant force (upward thrust):

• Since 25% of ice is outside the fluid, hence 75% is inside the fluid.

$\therefore \: mg = V_{in} \: \rho g$

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

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

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

$\implies \: \dfrac{ 930}{ \rho} = \dfrac{75\% \: V_{total}}{V_{total}}$

$\implies \: \dfrac{ 930}{ \rho} = \dfrac{75}{100}$

$\implies \: \dfrac{ 930}{ \rho} = \dfrac{3}{4}$

$\implies \: \dfrac{310}{ \rho} = \dfrac{1}{4}$

$\implies \: \rho = 310 \times 4$

$\implies \: \rho = 1240 \: kg/ {m}^{3}$

$\implies \: \rho = 1.24 \: g/ {cm}^{3}$

So, density of fluid is 1.24 g/cm³.