Solved Examples of Archimedes' Principle: Step-by-Step Solutions

📚 Quick Study Guide

• 🌊 Archimedes' Principle: States that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.
• ⚖️ Buoyant Force ($F_B$): The upward force exerted by a fluid that opposes the weight of an immersed object.
• 📏 Formula: $F_B = \rho V g$, where $\rho$ is the density of the fluid, $V$ is the volume of the fluid displaced by the object, and $g$ is the acceleration due to gravity.
• 💧 Density ($\rho$): Mass per unit volume. $\rho = \frac{m}{V}$
• 🌎 Gravity (g): Acceleration due to gravity, approximately $9.8 m/s^2$ on Earth.
• 🧊 Apparent Weight: The weight of an object submerged in a fluid is less than its weight in air due to the buoyant force. Apparent weight = Actual weight - Buoyant force.

🧪 Practice Quiz

1. Question 1: A stone weighs 5 N in air and 3 N when immersed in water. What is the buoyant force acting on the stone?
   1. 2 N
   2. 3 N
   3. 5 N
   4. 8 N
2. Question 2: A block of wood has a volume of 200 $cm^3$ and a density of 800 $kg/m^3$. What percentage of the block's volume is submerged when it floats in water (density 1000 $kg/m^3$) ?
   1. 60%
   2. 80%
   3. 20%
   4. 100%
3. Question 3: A metal object weighs 50 N in air and 30 N when fully submerged in water. What is the volume of the object? (Density of water = 1000 $kg/m^3$, g = 9.8 $m/s^2$)
   1. 0.00204 $m^3$
   2. 0.00510 $m^3$
   3. 0.00306 $m^3$
   4. 0.00408 $m^3$
4. Question 4: A balloon has a volume of 1 $m^3$ and is filled with helium (density = 0.18 $kg/m^3$). If the density of air is 1.29 $kg/m^3$, what is the buoyant force acting on the balloon?
   1. 1.29 N
   2. 12.64 N
   3. 129 N
   4. 1264 N
5. Question 5: An object floats with 1/4 of its volume above the water surface. What is the density of the object if the density of water is 1000 $kg/m^3$?
   1. 250 $kg/m^3$
   2. 750 $kg/m^3$
   3. 1250 $kg/m^3$
   4. 500 $kg/m^3$
6. Question 6: A cube with sides of 0.1 m is submerged in a liquid with a density of 1500 $kg/m^3$. What is the buoyant force on the cube?
   1. 1.47 N
   2. 14.7 N
   3. 147 N
   4. 1470 N
7. Question 7: A piece of metal weighs 90 g in air and 80 g when immersed in water. Calculate its relative density.
   1. 7
   2. 8
   3. 9
   4. 10