Floatation and Buoyancy Solved Examples (Class 9 Physics)
Floatation numericals apply Archimedes' principle to determine if objects float and calculate buoyant forces. These problems explain why ships float and su
TL;DR: Floatation numericals apply Archimedes' principle to determine if objects float and calculate buoyant forces. These problems explain why ships float a…
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Floatation numericals apply Archimedes' principle to determine if objects float and calculate buoyant forces. These problems explain why ships float and su
Floatation and Buoyancy — Solved Numerical Examples (Step by Step)
Example 1: A wooden block of volume 0.5 m³ is fully submerged in water. Calculate the buoyant force. (Density of water = 1000 kg/m³, g = 10 m/s²)
Solution: Volume = 0.5 m³, Density of water = 1000 kg/m³, g = 10 m/s². Buoyant force = Density × g × Volume = 1000 × 10 × 0.5 = 5000 N.
Example 2: A cork of mass 0.2 kg and density 200 kg/m³ is placed in water. Will it float? (Density of water = 1000 kg/m³)
Solution: Density of cork = 200 kg/m³ is less than density of water = 1000 kg/m³. Since cork is less dense than water, it will float.
Example 3: A steel ball of mass 100 kg is completely submerged in water. Calculate the buoyant force. (Density of water = 1000 kg/m³, g = 10 m/s², Density of steel = 8000 kg/m³)
Solution: Mass of ball = 100 kg, Density of steel = 8000 kg/m³. Volume = Mass / Density = 100 / 8000 = 0.0125 m³. Buoyant force = 1000 × 10 × 0.0125 = 125 N.
Example 4: A ship displaces 50,000 m³ of water. Calculate the buoyant force. (Density of water = 1000 kg/m³, g = 10 m/s²)
Solution: Volume displaced = 50,000 m³, Density of water = 1000 kg/m³, g = 10 m/s². Buoyant force = 1000 × 10 × 50,000 = 500,000,000 N = 5 × 10^8 N.
Example 5: A floating object has its 0.6 of volume submerged in water. If the object has volume 2 m³, what is the buoyant force? (Density of water = 1000 kg/m³, g = 10 m/s²)
Solution: Volume submerged = 0.6 × 2 = 1.2 m³. Buoyant force = 1000 × 10 × 1.2 = 12,000 N.
Example 6: A balloon filled with helium has total volume 5 m³. The balloon material weighs 50 N. Calculate the net upward force. (Density of air = 1.2 kg/m³, Density of helium = 0.18 kg/m³, g = 10 m/s²)
Solution: Buoyant force from air = 1.2 × 10 × 5 = 60 N. Weight of helium = 0.18 × 10 × 5 = 9 N. Weight of balloon = 50 N. Net upward force = 60 - 9 - 50 = 1 N.
Tips
- Archimedes' principle: Buoyant force equals weight of displaced fluid.
- An object floats if its density is less than the fluid's density.
- Fully submerged objects experience maximum buoyant force.
Frequently Asked Questions
Why do some things float while others sink?
Objects with density less than water float because the buoyant force exceeds their weight. Objects denser than water sink because their weight exceeds buoyant force.
Does the size of a floating object matter?
Yes. A larger object displaces more water, experiencing greater buoyant force. However, it must still have overall density less than water to float.
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