If error in the masurement of mass is `0.8` of and in volume it is `0.4%` then error in the measurement of density is

Options

A. `1.2%`
B. `0.4%`
C. `0.8%`
D. `1%`

Explanation

To solve the problem of finding the error in the measurement of density given the errors in mass and volume, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Density**:
The formula for density (ρ) is given by:
\[ \rho = \frac{m}{V} \]
where \(m\) is mass and \(V\) is volume.

2. **Identify the Given Errors**:
- The error in mass measurement is given as \(0.8\%\).
- The error in volume measurement is given as \(0.4\%\).

3. **Express the Errors in Terms of Change**:
- The relative error in mass (\(\frac{\Delta m}{m}\)) can be expressed as:
\[ \frac{\Delta m}{m} \times 100 = 0.8 \implies \frac{\Delta m}{m} = \frac{0.8}{100} = 0.008 \]
- The relative error in volume (\(\frac{\Delta V}{V}\)) can be expressed as:
\[ \frac{\Delta V}{V} \times 100 = 0.4 \implies \frac{\Delta V}{V} = \frac{0.4}{100} = 0.004 \]

4. **Calculate the Error in Density**:
The formula for the error in density is given by:
\[ \frac{\Delta \rho}{\rho} = \frac{\Delta m}{m} + \frac{\Delta V}{V} \]
Substituting the values we calculated:
\[ \frac{\Delta \rho}{\rho} = 0.008 + 0.004 = 0.012 \]

5. **Convert the Relative Error to Percentage**:
To express the error in density as a percentage:
\[ \text{Error in density} = 0.012 \times 100 = 1.2\% \]

6. **Conclusion**:
The error in the measurement of density is \(1.2\%\).

### Final Answer:
The error in the measurement of density is \(1.2\%\).

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