Suppose a 5​-m cylindrical bar has a constant density of 2 ​g/cm for its left half and a constant density 3 ​g/cm for its right half. What is its​ mass?
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Part 1
The mass of the bar is 
  
enter your response here g. 

To find the total mass of the cylindrical bar, we need to calculate the mass of each half separately and then add them together. The bar has two different density values for its two halves.

### Given:
- **Length of the cylindrical bar**: 5 m = 500 cm (since 1 m = 100 cm)
- **Density of the left half**: 2 g/cm
- **Density of the right half**: 3 g/cm
- Each half of the bar has a length of \( \frac{500}{2} = 250 \, \text{cm} \).

### Mass of each half:
1. **Left half** (first 250 cm):
   - Density = 2 g/cm
   - Length = 250 cm
   - Mass of left half \( = 2 \, \text{g/cm} \times 250 \, \text{cm} = 500 \, \text{g} \)

2. **Right half** (next 250 cm):
   - Density = 3 g/cm
   - Length = 250 cm
   - Mass of right half \( = 3 \, \text{g/cm} \times 250 \, \text{cm} = 750 \, \text{g} \)

### Total mass:
\[
\text{Total mass} = 500 \, \text{g} + 750 \, \text{g} = 1250 \, \text{g}
\]

Thus, the mass of the bar is **1250 g**.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How would the total mass change if the entire bar had a constant density of 3 g/cm?
2. What would the mass be if the bar's total length was 10 meters but with the same density distribution?
3. How can we calculate the center of mass of this bar given the density variation?
4. What if the density on the left and right halves changed continuously instead of being constant?
5. How does the volume of the bar factor into the calculation if the radius were provided?

**Tip:** Always convert all units to the same system (e.g., cm) before performing calculations to avoid errors.

Suppose a 5​-m cylindrical bar has a constant density of 2 ​g/cm for its left half and a constant density of 3 ​g/cm for its right half. What is its​ mass?

Learn how to calculate the mass of a 5-meter cylindrical bar with varying densities of 2 g/cm for the left half and 3 g/cm for the right half. The problem involves unit conversion and basic mass calculations. Suitable for Grades 6-8 students.

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