The mass of a piece of cork is 20g. What fraction of the cork is immersed when it floats in water? (Take density of cork to be 0.25g/cm³)

1 answer

To find the fraction of the cork that is immersed when it floats in water, we need to compare the density of the cork to the density of water.

Density = Mass / Volume

Since the mass of the cork is given as 20g and the density of cork is given as 0.25g/cm³, we can calculate the volume of the cork.

Volume = Mass / Density
Volume = 20g / 0.25g/cm³

Converting grams to cubic centimeters, we have:
Volume = 20g / (0.25g/cm³) = 80 cm³

Now, to find the fraction of the cork that is immersed in water, we need to compare the volume of the immersed part to the total volume of the cork.

Let x be the volume of the immersed part.

Fraction of cork immersed = x / total volume of the cork
Fraction of cork immersed = x / 80 cm³

Now, we know that the cork is floating in water, which means that it displaces its own weight in water. This implies that the weight of the water displaced is equal to the weight of the cork.

Weight of water displaced = Weight of the cork
Density of water × Volume of water displaced = Mass of the cork
1g/cm³ × Volume of water displaced = 20g

Volume of water displaced = 20 cm³

Since the volume of water displaced is equal to the volume of the immersed part of the cork, we have:
x = 20 cm³

Fraction of cork immersed = x / 80 cm³
Fraction of cork immersed = 20 cm³ / 80 cm³
Fraction of cork immersed = 1/4

Therefore, the fraction of the cork that is immersed when it floats in water is 1/4.