Question

An empty spice bottle has an inner volume of 1.31 ´ 10-4 m3. It has a mass of 112 g when filled with air, and it displaces 1.63 ´ 10-4 m3 of water when fully submerged. What fraction of the total volume of the bottle will be beneath the surface when it is placed in a tank of water?

Answer 1

The fraction of the total volume of the bottle will be beneath the surface is 0.687

Step-by-step explanation:

The immersed volume is equal to:

`mg=V_(imm) *\rho _(water) *g\\V_(imm)=(m)/(\rho _(water))`

Where

m = 112 g = 0.112 kg

ρwater = 1000 kg/m³

Replacing:

`V_(imm) =(0.112)/(1000) =1.12x10^(-4) m^(3)`

The fraction of the total volume of the bottle will be beneath the surface is:

`fraction=(1.12x10^(-4) )/(1.63x10^(-4) ) =0.687`