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A ball weighing 4 kg with a density of 4000 kg/m\(^3\) is completely immersed in water with a density of 103 kg/m\(^3\). Find the force of buoyancy on it. (Given \(g = 10 \, \text{m/s}^2\))

Answer :

The buoyant force acting on a ball completely submerged in water is calculated through Archimedes' principle and is found to be 10 Newtons.

To calculate the force of buoyancy on a ball when it is completely submerged in water, we apply Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. Since the ball has a density of 4000 kg/m3, to find the volume of the ball, we use the formula for density (Density = Mass/Volume), thus Volume = Mass/Density. With the mass of the ball being 4 kg:

Volume = 4 kg / 4000 kg/m3 = 0.001 m3

The weight of water displaced can then be calculated with the water's density and the volume of the ball:

Mass of displaced water = Volume \\* Density of water = 0.001 m3 \\* 1000 kg/m3 = 1 kg

Finally, applying the buoyant force formula (Buoyant Force = Mass of displaced water \\* g), where g is the acceleration due to gravity:

Buoyant Force = 1 kg \\* 10 m/s2 = 10 N

Thus, the buoyant force acting on the ball is 10 Newtons.

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