Solved Floatation Numericals with Tips | Physics Exam Success

Floatation Numericals

Practice these ten solved numericals on floatation to build your calculation skills and master the topic for exams. Click each problem to reveal a detailed solution and expert tip.

Concept Recap: What is Floatation?

Floatation occurs when an object is partially or fully submerged in a fluid and is acted upon by an upward force called buoyant force. This force is equal to the weight of the fluid displaced by the object. The principles of floatation are used in designing ships, submarines, hydrometers, and even in understanding why icebergs float!

Solved Floatation Numericals

Each numerical below is based on real exam patterns and covers a variety of floatation concepts. Click on any numerical to check the step-by-step solution and a helpful tip.

1. A block of wood of mass 0.6 kg floats in water. Calculate the buoyant force acting on the block. (g = 9.8 m/s²)

Solution: For a floating object, the buoyant force equals the weight of the block.
Weight = mass × g = 0.6 kg × 9.8 m/s² = 5.88 N.
Tip: For floating objects, buoyant force always equals the object's weight.

2. An object weighs 40 N in air and 30 N when fully immersed in water. Find the upthrust and the weight of water displaced.

Solution: Upthrust = Weight in air - Weight in water = 40 N - 30 N = 10 N.
The upthrust equals the weight of water displaced, so the answer is 10 N.
Tip: Upthrust is always equal to the weight of liquid displaced.

3. A 250 g piece of metal displaces 150 cm³ of water when fully submerged. What is the density of the metal? (Density = mass/volume)

Solution: Convert mass to grams (already in g) and volume to cm³ (already in cm³).
Density = 250 g / 150 cm³ = 1.67 g/cm³.
Tip: Always check units before calculating density.

4. A block of volume 200 cm³ floats in oil with 150 cm³ submerged. What is the density of oil if the block's density is 600 kg/m³?

Solution: Fraction submerged = density of block / density of liquid.
150/200 = 600 / density of oil ⇒ density of oil = (600 × 200) / 150 = 800 kg/m³.
Tip: The more an object is submerged, the closer its density is to the fluid's density.

5. An ice cube of volume 30 cm³ floats in water. What volume of water does it displace? (Density of ice = 0.92 g/cm³, water = 1 g/cm³)

Solution: Fraction submerged = density of ice / density of water = 0.92/1 = 0.92.
Volume displaced = 0.92 × 30 cm³ = 27.6 cm³.
Tip: For floating objects, the volume submerged = (object density)/(fluid density) × total volume.

6. A body of mass 2 kg and volume 0.0025 m³ is completely immersed in a liquid of density 800 kg/m³. Find the upthrust on the body. (g = 10 m/s²)

Solution: Upthrust = volume × density of liquid × g = 0.0025 × 800 × 10 = 20 N.
Tip: Use the formula: Upthrust = V × ρ × g.

7. A solid sphere of volume 100 cm³ is placed in a liquid of density 1.2 g/cm³. What is the maximum buoyant force it can experience? (g = 9.8 m/s²)

Solution: Max buoyant force = weight of liquid displaced = volume × density × g.
Convert density to kg/m³: 1.2 g/cm³ = 1200 kg/m³; volume = 100 cm³ = 0.0001 m³.
Buoyant force = 0.0001 × 1200 × 9.8 = 1.176 N.
Tip: Convert all units to SI before calculation.

8. A 500 g object floats in a liquid, displacing 400 g of the liquid. What is the relative density of the object?

Solution: Relative density = weight of object / weight of liquid displaced = 500 g / 400 g = 1.25.
Tip: For floating objects, relative density = mass of object / mass of displaced liquid.

9. A block floats in water with 60% of its volume submerged. If the block's volume is 250 cm³, what is its density?

Solution: Fraction submerged = density of block / density of water.
0.6 = density / 1 (since water is 1 g/cm³). So, density = 0.6 g/cm³.
Tip: The percentage of volume submerged gives you the ratio of densities directly.

10. A 2 kg object is completely immersed in a liquid of density 900 kg/m³. If the volume of the object is 0.002 m³, calculate the loss of weight of the object. (g = 10 m/s²)

Solution: Loss of weight = upthrust = volume × density of liquid × g = 0.002 × 900 × 10 = 18 N.
Tip: The loss of weight equals the weight of the liquid displaced (i.e., the upthrust).

How Floatation Numericals Help in Exams

Solving numericals on floatation helps you understand the application of formulas and concepts in real-life situations and exam scenarios. Regular practice ensures you are confident and quick during tests.

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Shaleen Shekhar | The Physics Next