Question

An object is solid throughout. When the object is completely submerged in ethyl alcohol, its apparent weight is 15.9 N. When completely submerged in water, its apparent weight is 13.4 N. What is the volume of the object?

Answer 1

Given that

An object is solid throughout. When the object is completely submerged in ethyl alcohol, its apparent weight is 15.9 N

When completely submerged in water, its apparent weight is 13.4 N.

We also know that

The density of water )pwater)=1000kg/m³

Density of alchol is(palcohol) =806kg/m³

and the acceleration due to gravity (g) =9.8m/s²

We know that when an objectis completely submerged in within a fluid, its apparent weight in the fluid is equal to the its true weight mg minus the upward acting buoyant force.

Now from the Archimedes principle, the magnitude of the buoyant force is equal to the weight of the fluid displaced by the object.The weight of the fluid displaced by the object is based on the volume of the object.

Now the Apparent weight is given by

15.9N =mg -palcoholgV-------(1)

13.4N=mg -pwatergV-----------(2)

Now from the equation (1) and (2) the volume of the object is given by

V =(15.9-13.4)/g(pwater-palcohol) =2.5/9.81(1000-806) =1.313*10^-3m³