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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 the ball.

(Given: g = 10 m s⁻².)

Answer :

The buoyant force on the 4 kg ball immersed in water is 1.03 N, given the density of water and gravity.

To find the buoyant force on the ball immersed in water, we'll use Archimedes' principle, which states that the buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.

The buoyant force (B) can be calculated using the formula:

[tex]\[ B = \rho_{\text{fluid}} \times V_{\text{displaced}} \times g \][/tex]

Where:

[tex]- \( \rho_{\text{fluid}} \) is the density of the fluid (water in this case).[/tex]

[tex]- \( V_{\text{displaced}} \) is the volume of the fluid displaced by the object.[/tex]

[tex]- \( g \) is the acceleration due to gravity.[/tex]

First, let's calculate the volume of the ball submerged in water. Since the ball is completely submerged, the volume of the fluid displaced is equal to the volume of the ball.

The density of the ball [tex](\( \rho_{\text{ball}} \))[/tex] is given by:

[tex]\[ \rho_{\text{ball}} = \frac{m}{V_{\text{ball}}} \][/tex]

Where:

[tex]- \( m \) is the mass of the ball.[/tex]

[tex]- \( V_{\text{ball}} \) is the volume of the ball.[/tex]

Given that the mass of the ball (m) is 4 kg, and the density of the ball is 4000 kg/m³, we can rearrange the equation to find the volume of the ball:

[tex]\[ V_{\text{ball}} = \frac{m}{\rho_{\text{ball}}} \][/tex]

[tex]\[ V_{\text{ball}} = \frac{4 \, \text{kg}}{4000 \, \text{kg/m}^3} \][/tex]

[tex]\[ V_{\text{ball}} = 0.001 \, \text{m}^3 \][/tex]

Now that we have the volume of the ball, we can calculate the buoyant force:

[tex]\[ B = \rho_{\text{fluid}} \times V_{\text{ball}} \times g \][/tex]

Given:

- [tex]\( \rho_{\text{fluid}} \)[/tex] = 103 kg/m³ (density of water)

- [tex]\( V_{\text{ball}} \)[/tex] = 0.001 m³

- [tex]\( g \)[/tex] = 10 m/s²

Substituting the values:

[tex]\[ B = 103 \, \text{kg/m}^3 \times 0.001 \, \text{m}^3 \times 10 \, \text{m/s}^2 \][/tex]

[tex]\[ B = 1.03 \, \text{N} \][/tex]

So, the buoyant force on the ball immersed in water is [tex]\( 1.03 \, \text{N} \)[/tex].

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Rewritten by : Barada