**Understanding Buoyancy and Density: A Rock's Investigation****Introduction:**A rock with a mass of **546 g** in air is found to have an apparent mass of **344 g** when submerged in water.**Questions to Explore:****(a) What mass (in g) of water is displaced?**\[ \_\_\_\_\_\_ g \]**(b) What is the volume (in cm³) of the rock?**\[ \_\_\_\_\_\_ cm³ \]**(c) What is its average density (in g/cm³)?**\[ \_\_\_\_\_\_ g/cm³ \]Is this consistent with the value for granite?- Yes- No**Explanation:**1. **Mass of Water Displaced:** - Since the rock appears lighter in water due to the displaced water, the mass of the displaced water is the difference between the mass of the rock in air and its apparent mass in water. - Mass of water displaced = \( 546 \, \text{g} - 344 \, \text{g} = 202 \, \text{g} \).2. **Volume of the Rock:** - By Archimedes' principle, the mass of the displaced water equals the volume of the rock (since the density of water is 1 g/cm³). - Volume of the rock = \( 202 \, \text{cm}^3 \).3. **Average Density of the Rock:** - Density (\( \rho \)) can be calculated using the formula: \( \rho = \frac{\text{Mass}}{\text{Volume}} \). - Density of the rock = \( \frac{546 \, \text{g}}{202 \, \text{cm}^3} \approx 2.70 \, \text{g/cm}^3 \).**Conclusion:**Verify if the calculated density is consistent with the known value for granite. Most granites have a density ranging from 2.63 to 2.75 g/cm³, so a density of approximately 2.70 g/cm³ aligns well with the typical range for granite.

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Description: **Understanding Buoyancy and Density: A Rock's Investigation****Introduction:**A rock with a mass of **546 g** in air is found to have an apparent mass of **344 g** when submerged in water.**Questions to Explore:****(a) What mass (in g) of water is

In the given question, Mass of rock in air (ma) = 546g = 0.546kg Mass of rock in water (mw) = 344g =…

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A rock with a mass of 546 g in air is found to have an apparent mass of 344 g when submerged in water. (a) What mass (in g) of water is displaced? g (b) What is the volume (in cm³) of the rock? cm3 (c) What is its average density (in g/cm³)? 9/cm3

A rock with a mass of 546 g in air is found to have an apparent mass of 344 g when submerged in water. (a) What mass (in g) of water is displaced? g (b) What is the volume (in cm³) of the rock? cm3 (c) What is its average density (in g/cm³)? 9/cm3

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Chapter1: Units, Trigonometry. And Vectors

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Question

**Understanding Buoyancy and Density: A Rock's Investigation**

**Introduction:**
A rock with a mass of **546 g** in air is found to have an apparent mass of **344 g** when submerged in water.

**Questions to Explore:**

**(a) What mass (in g) of water is displaced?**

\[ \_\_\_\_\_\_ g \]

**(b) What is the volume (in cm³) of the rock?**

\[ \_\_\_\_\_\_ cm³ \]

**(c) What is its average density (in g/cm³)?**

\[ \_\_\_\_\_\_ g/cm³ \]

Is this consistent with the value for granite?

- Yes
- No

**Explanation:**
1. **Mass of Water Displaced:**
- Since the rock appears lighter in water due to the displaced water, the mass of the displaced water is the difference between the mass of the rock in air and its apparent mass in water.
- Mass of water displaced = \( 546 \, \text{g} - 344 \, \text{g} = 202 \, \text{g} \).

2. **Volume of the Rock:**
- By Archimedes' principle, the mass of the displaced water equals the volume of the rock (since the density of water is 1 g/cm³).
- Volume of the rock = \( 202 \, \text{cm}^3 \).

3. **Average Density of the Rock:**
- Density (\( \rho \)) can be calculated using the formula: \( \rho = \frac{\text{Mass}}{\text{Volume}} \).
- Density of the rock = \( \frac{546 \, \text{g}}{202 \, \text{cm}^3} \approx 2.70 \, \text{g/cm}^3 \).

**Conclusion:**
Verify if the calculated density is consistent with the known value for granite. Most granites have a density ranging from 2.63 to 2.75 g/cm³, so a density of approximately 2.70 g/cm³ aligns well with the typical range for granite.

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