Question

A sample of an unknown material appears to weigh 300 N in air and 180 N when immersed in alcohol of specific gravity 0.700.

(a) What is the volume of the material?
? m^3

(b) What is the density of the material?
? kg/m³

Answer 1

Because the material weighs 180N when immersed in alcohol, that means the buoyancy force acting upon it is 300-180 = 120N
Then, we can use the following formula:
F = pVg, where F = buoyancy force
p = density of fluid, in this case, alcohol
V = volume displaced (assume completely immersed)
g = acceleration due to gravity

(A)

F = pVg
120 = (0.700)V(9.81)
V = 17.4927 m^3 = volume

(B)

You also know that pV = m, where
p = density of unknown material
V = volume of material
m = mass, which can be found using F = mg
Since we known it material weighs 300N in air:
F = mg
300 = m(9.8) , m = 30.61 kg

Therefore,

pV = m
p(17.4927) = 30.61
p = 1.749 kg/m^3 = density