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Exploring Forces - Floating and Sinking

Grade 8CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Buoyancy: When an object is immersed in a fluid (liquid or gas), it experiences an upward force called the buoyant force or upthrust (FBF_{B}).

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Archimedes' Principle: It states that when a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.

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Density (ρ\rho): It is defined as the mass per unit volume of a substance. The SI unit of density is kg/m3kg/m^3.

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Relative Density: It is the ratio of the density of a substance to the density of water at 4∘C4^{\circ}C. It has no units.

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Law of Floatation: An object floats if the buoyant force exerted by the liquid is equal to the weight of the object (W=FBW = F_{B}). Alternatively, an object floats if its density ρobject≤ρfluid\rho_{object} \le \rho_{fluid}.

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Sinking: An object sinks if its weight (WW) is greater than the buoyant force (FBF_{B}), or if its density is greater than the density of the fluid.

📐Formulae

Density (ρ)=Mass (m)Volume (V)\text{Density } (\rho) = \frac{\text{Mass } (m)}{\text{Volume } (V)}

Relative Density=Density of substanceDensity of water\text{Relative Density} = \frac{\text{Density of substance}}{\text{Density of water}}

FB=V⋅ρf⋅gF_{B} = V \cdot \rho_{f} \cdot g

Weight in fluid=Weight in air−Buoyant force\text{Weight in fluid} = \text{Weight in air} - \text{Buoyant force}

💡Examples

Problem 1:

An object of mass 500 g500\text{ g} has a volume of 250 cm3250\text{ cm}^3. Calculate its density and determine if it will float or sink in water (Density of water = 1 g/cm31\text{ g/cm}^3).

Solution:

Density ρ=mV=500250=2 g/cm3\rho = \frac{m}{V} = \frac{500}{250} = 2\text{ g/cm}^3. Since 2 g/cm3>1 g/cm32\text{ g/cm}^3 > 1\text{ g/cm}^3, the object will sink.

Explanation:

The density of the object is greater than the density of water, so the gravitational force (weight) overcomes the maximum buoyant force the water can provide.

Problem 2:

A metal block weighs 800 N800\text{ N} in air and 650 N650\text{ N} when fully immersed in water. Find the buoyant force acting on the block.

Solution:

The buoyant force is the difference between the weight in air and the weight in water: 800−650150\begin{array}{r} 800 \\ - 650 \\ \hline 150 \end{array} The buoyant force is 150 N150\text{ N}.

Explanation:

According to Archimedes' principle, the loss in weight of the object is equal to the buoyant force (upthrust) exerted by the fluid.

Problem 3:

Calculate the relative density of silver if its density is 10800 kg/m310800\text{ kg/m}^3 and the density of water is 1000 kg/m31000\text{ kg/m}^3.

Solution:

Relative Density=108001000=10.8\text{Relative Density} = \frac{10800}{1000} = 10.8

Explanation:

Relative density is a pure ratio obtained by dividing the density of the substance by the density of water, hence it has no units.