The problem involves determining the upthrust (buoyant force) acting on a body floating in a liquid.

We know the following information:

• Mass of the body, $m = 20 \, \text{g}$
• Volume of the body, $V = 60 \, \text{cm}^3$
• Density of the liquid, $\rho_{\text{liquid}} = 0.8 \, \text{g/cm}^3$

Step 1: Archimedes' Principle

The upthrust or buoyant force on a body floating in a liquid is given by Archimedes' principle, which states:

$\text{Upthrust} = \text{weight of liquid displaced}$

The weight of the displaced liquid can be calculated as:

$\text{Upthrust} = V_{\text{body}} \times \rho_{\text{liquid}} \times g$

Where:

• $V_{\text{body}}$ is the volume of the body (equal to the volume of liquid displaced),
• $\rho_{\text{liquid}}$ is the density of the liquid,
• $g$ is the acceleration due to gravity (usually taken as $9.8 \, \text{m/s}^2$).

Step 2: Calculating the Upthrust

Substituting the given values:

$\text{Upthrust} = 60 \, \text{cm}^3 \times 0.8 \, \text{g/cm}^3 \times 9.8 \, \text{m/s}^2$

First, we calculate the product of volume and density:

$60 \times 0.8 = 48 \, \text{g}$

Next, we calculate the upthrust in terms of force (converting mass to weight using $g = 9.8$):

$\text{Upthrust} = 48 \times 9.8 = 470.4 \, \text{dyne} \, (\text{since} \, 1 \, \text{g cm/s}^2 = 1 \, \text{dyne})$

Thus, the upthrust on the body is approximately 470.4 dyne.

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Would you like more details on any of the steps? Here are 5 questions to expand your understanding:

1. What is Archimedes' principle, and how is it applied in this problem?
2. How does the density of a liquid affect the buoyant force on a floating body?
3. What would happen to the upthrust if the liquid had a higher density?
4. Why is the acceleration due to gravity (g) involved in calculating upthrust?
5. How does the concept of upthrust relate to the stability of floating objects?

Tip: Upthrust depends on the volume of liquid displaced, not the mass of the floating object itself!