Question

a sample of unknown material weighs 500 n in air and 200 n when immesersed in alcholol with a specfic gravity of 0.7 what is the mass density

Answer 1

Answer: The mass density is 1166.36 $kg/m^{3}$.

Explanation:

Given: Weight of sample in air $(F_{air})$ = 500 N

Weight of sample in alcohol $(F_{alc})$ = 200 N

Specific gravity = 0.7 = $0.7 \times 1000 = 700 kg/m^{3}$

Formula used to calculate Buoyant force is as follows.

$F_{B} = F_{air} - F_{alc}\\= 500 - 200 \\= 300 N$

Hence, volume of the material is calculated as follows.

$V = \frac{F_{B}}{\rho \times g}$

where,

$F_{B}$ = Buoyant force

$\rho$ = specific gravity

g = acceleration due to gravity = 9.81

Substitute the values into above formula.

$V = \frac{F_{B}}{\rho \times g}\\= \frac{300}{700 \times 9.81}\\= \frac{300}{6867}\\= 0.0437 m^{3}$

Now, mass of the material is calculated as follows.

$mass = \frac{F_{air}}{g}\\= \frac{500 N}{9.81}\\= 50.97 kg$

Therefore, density of the material or mass density is as follows.

$Density = \frac{mass}{volume}\\= \frac{50.97 kg}{0.0437 m^{3}}\\= 1166.36 kg/m^{3}$

Thus, we can conclude that the mass density is 1166.36 $kg/m^{3}$.