Question

A $6.00-cm$-diameter sphere with a mass of$89.3g$ is neutrally buoyant in a liquid. Identify the liquid.

Short answer

In Ethanol,$6cm$diameter sphere with a mass of$89.3g$is neutrally beyond.

Step-by-step solution

Ethanol.

Ethanol is a plant-based fuel manufactured from corn and other plants.

Ethanol is widely used, with ethanol present in more than $98$a percent of gasoline sold in the United States. $E10$is the most prevalent ethanol blend ($10$percent ethanol, $90$percent gasoline)

The density.

We must identify the liquid by determining its density in this scenario.

The weight of a sphere is equal to the buoyant force acting on a body since it is neutrally buoyant. The density can be expressed as follows based on this equality:

$$\begin{gathered} mg=\rho gV \\ \Rightarrow \rho =\frac{m}{\left(\frac{4}{3}\pi R^3\right)} \\ =\frac{m}{\frac{4}{3}\pi {\left(\frac{D}{2}\right)}^3} \\ =\frac{6m}{\pi D^3} \end{gathered}$$

Find the liquid.

We have created our own values by substituting our own values.

$\rho =\frac{6\times 0.0893}{\pi \times 0.{06}^3}$

$=790kg/m^3$

We can see from the data that Ethanol has a density of 790kg/m, $C_2{H}_{5}OH$