An aluminum cylinder with a density of 2.70 g/cm3 has a volume of 3.8 ¡¿ 10-5 m3. If the cylinder is suspended from a scale and immersed in an unknown fluid, the scale reads 0.581 N? What is the specific gravity of the fluid?

The actual mass of the cylinder is

(density)*(volume)
= 2700 kg/m^3*3.8*10^-5 m^3
= 0.1026 kg
and its weight is M g = 1.007 N

The reduction in weight when immersed, 0.426 N, equals the buoyancy, which is the displaced fluid weight.

The density of the fluid is given by
(density)*g*V = 0.426 N
density = 1.143*10^3 kg/m^3

Divide that by the density of water for the specific gravity of the immersion fluid.

To find the specific gravity of the fluid, we need to compare the density of the fluid to the density of water.

The specific gravity (SG) of a substance is defined as the ratio of its density to the density of water. The density of water is 1000 kg/m^3 or 1 g/cm^3.

To find the density of the fluid, we can use the formula:

Density = Mass / Volume

The mass of the fluid can be calculated by multiplying the density of the aluminum cylinder by its volume:

Mass = Density x Volume

Next, we can calculate the density of the fluid by rearranging the formula:

Density of the fluid = Mass of the fluid / Volume of the fluid

Now, let's calculate the mass of the fluid:

Density of the aluminum cylinder = 2.70 g/cm^3
Volume of the aluminum cylinder = 3.8 x 10^(-5) m^3

Mass of the aluminum cylinder = Density x Volume
= 2.70 g/cm^3 x 3.8 x 10^(-5) m^3

We need to convert the volume from cubic meters to cubic centimeters to match the units of the density:

1 m^3 = 10^6 cm^3 (since 1 m = 100 cm)

Volume of the aluminum cylinder = 3.8 x 10^(-5) m^3 x (10^6 cm^3 / 1 m^3)
= 3.8 x 10^1 cm^3

Mass of the aluminum cylinder = 2.70 g/cm^3 x 3.8 x 10^1 cm^3
= 102.6 g

Next, let's calculate the density of the fluid:

Density of the fluid = Mass of the fluid / Volume of the fluid
= (Mass of the aluminum cylinder - Mass of the fluid) / Volume of the fluid

We need to find the mass of the fluid, which equals the weight of the aluminum cylinder minus the scale reading:

Weight of the aluminum cylinder = 0.581 N (given)
Mass of the fluid = Weight of the aluminum cylinder / acceleration due to gravity (g)

To convert the weight from Newtons to kilograms, we need to divide it by the acceleration due to gravity, which is approximately 9.8 m/s^2:

Mass of the fluid = 0.581 N / 9.8 m/s^2
= 0.059 kg

Now, let's calculate the density of the fluid:

Density of the fluid = (Mass of the aluminum cylinder - Mass of the fluid) / Volume of the fluid
= (102.6 g - 59 g) / 3.8 x 10^(-5) m^3

We need to convert the mass from grams to kilograms, and the volume from cubic meters to cubic centimeters:

Density of the fluid = (102.6 g - 59 g) / (3.8 x 10^(-5) m^3 x 10^6 cm^3 / 1 m^3)

Density of the fluid = 43.6 g / (3.8 x 10^(-5) m^3 x 10^6 cm^3 / 1 m^3)
= 43.6 g / 3.8 cm^3
= 11.474 g/cm^3

Finally, we can calculate the specific gravity of the fluid:

Specific gravity of the fluid = Density of the fluid / Density of water
= 11.474 g/cm^3 / 1 g/cm^3
= 11.474

Therefore, the specific gravity of the fluid is 11.474.