Question

A cork weighing 2.5 gf in air is tied to a sinker, resulting in a total weight of 20 gf in water. If the sinker alone weighs 25 gf in water, find the density of the cork.

a) 0.5 g/cm^3
b) 1.5 g/cm^3
c) 2.0 g/cm^3
d) 2.5 g/cm^3

Answer 1

To find the density of the cork, calculate its apparent loss of weight in water and then use the formula for density. The density of the cork is 0.33 g/gf.

Step-by-step explanation:

To find the density of the cork, we can use the principle of buoyancy. The weight of the cork in air is 2.5 grams-force (gf), and the total weight in water is 20 gf. We know that the weight of the sinker alone in water is 25 gf. So, the weight of the cork in water is 20 - 25 = -5 gf. The negative sign indicates that the cork is buoyant, meaning it floats in water.

Now, to find the density of the cork, we can use the formula:

Density = mass / volume

Since we know the weight of the cork in air and its weight in water, we can calculate its apparent loss of weight in water:

Apparent Loss of Weight = Weight in Air - Weight in Water = 2.5 gf - (-5 gf) = 7.5 gf

According to Archimedes' principle, the apparent loss of weight is equal to the weight of the water displaced by the object. So, the volume of water displaced by the cork is 7.5 gf.

Now, we can substitute the values into the formula for density:

Density = mass / volume = 2.5 gf / 7.5 gf = 0.33 g/gf

Therefore, the density of the cork is 0.33 g/gf.