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)
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.
To determine the fraction of the cork that is immersed when it floats in water, we need to compare the buoyant force acting on the cork to the weight of the cork.
The buoyant force is equal to the weight of the water displaced by the cork.
First, let's determine the volume of the cork. The density of the cork is given as 0.25g/cm³. Since the mass of the cork is 20g, we can use the formula:
Volume = Mass / Density
Volume = 20g / 0.25g/cm³
Converting grams to cm³, we have:
Volume = 20cm³
Now, let's consider the weight of the cork. The weight of an object is given by the formula:
Weight = Mass * Gravitational Acceleration
Given that the mass of the cork is 20g and the gravitational acceleration is approximately 9.8 m/s², we can convert the mass to kilograms and calculate the weight:
Mass = 20g / 1000 = 0.02kg
Weight = 0.02kg * 9.8 m/s²
Weight = 0.196N
Since the cork is floating, the buoyant force is equal to the weight of the cork. Therefore, the fraction of the cork immersed can be calculated as:
Fraction Immersed = Weight of Water Displaced / Weight of Cork
The weight of the water displaced is equal to the buoyant force acting on the cork. Therefore, the fraction immersed can be found by dividing the weight of the water displaced by the weight of the cork.
Since the weight of the water displaced is equal to the weight of the cork, the fraction immersed is 1.
So, the entire cork is submerged in water when it floats.