Calculate the upthrust on a spherical ball of volume 4.2 x 10$^{-4}$m$^{3}$ when totally immersed in a liquid of density 1028kgm$^{-3}$

1. Analyze the Question

We are asked to calculate the upthrust (buoyant force) acting on a spherical ball that is completely submerged in a liquid.

Given data:

• Volume of the ball ($V$) = $4.2 \times 10^{-4} \, \text{m}^3$
• Density of the liquid ($\rho$) = $1028 \, \text{kg/m}^3$
• Acceleration due to gravity ($g$) = $9.8 \, \text{m/s}^2$ (standard constant used in JAMB Physics)

2. Explain the Concept

According to Archimedes' Principle, the upthrust on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.

The formula for upthrust ($U$) is:

Where:

• $V$ is the volume of the displaced fluid (which is equal to the volume of the submerged object).
• $\rho$ is the density of the fluid.
• $g$ is the acceleration due to gravity.

3. Show the Solution

Substitute the given values into the formula:

Step-by-step calculation:

1. Multiply the volume by the density: $4.2 \times 1028 = 4317.6$ $4317.6 \times 10^{-4} = 0.43176$

2. Multiply the result by gravity ($g = 9.8$): $0.43176 \times 9.8 = 4.231248 \, \text{N}$

Rounding this to one decimal place, we get approximately 4.23 N. Looking at the provided options, 4.3 N is the closest value.

4. Identify the Answer

Comparing our result to the options provided: A. 5.2N B. 4.3N C. 3.0N D. 2.4N

This is consistent with our calculation, as 4.23N rounds to 4.3N.

5. Tip

When solving buoyancy problems in JAMB, always ensure your units are in SI units (meters, kilograms, seconds). If the volume is given in $\text{cm}^3$, you must convert it to $\text{m}^3$ by multiplying by $10^{-6}$ before plugging it into the formula. Also, if the question doesn't specify $g$, always use $9.8 \, \text{m/s}^2$ or $10 \, \text{m/s}^2$ depending on which gives a result matching the options.