A body of mass 20gm and volume 60c * m ^ 3 floats in a liquid of density 0/8 * gm / c * m ^ 3 The upthrust on the body is

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!

A body of mass 20gm and volume 60cm^3 floats in a liquid of density 0.8gm/cm^3. The upthrust on the body is?

Calculate the upthrust on a body with mass 20g and volume 60cm³ floating in a liquid with density 0.8g/cm³. This problem explores the application of Archimedes' principle and buoyancy, suitable for students in Grades 9-12.

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