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 find the error in the measurement of density given the errors in mass and volume, we can follow these steps:

### Step 1: Understand the relationship between mass, volume, and density
Density (ρ) is defined as:
\[ \rho = \frac{m}{v} \]
where \(m\) is mass and \(v\) is volume.

### Step 2: Identify the errors in mass and volume
We are given:
- Error in mass measurement: \(\Delta m = 0.8\%\)
- Error in volume measurement: \(\Delta v = 0.4\%\)

### Step 3: Use the formula for error in density
The formula for the error in density can be derived from the relationship of density with mass and volume. The relative error in density is given by:
\[ \frac{\Delta \rho}{\rho} = \frac{\Delta m}{m} + \frac{\Delta v}{v} \]
This means that the percentage error in density is the sum of the percentage errors in mass and volume.

### Step 4: Substitute the known values
Now, substituting the known values of the errors:
\[ \frac{\Delta \rho}{\rho} = 0.8\% + 0.4\% \]

### Step 5: Calculate the total error in density
Adding the two errors together:
\[ \frac{\Delta \rho}{\rho} = 1.2\% \]

### Conclusion
The error in the measurement of density is \(1.2\%\).

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