If percentage errors in the measurement of mass and volume of an object are `2% and 3%` respectively, then the percentage error in the measurement of the density of the object is :

Options

A. `1%`
B. `0.66%`
C. `5%`
D. `6%`

Explanation

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

### Step-by-Step Solution:

1. **Understand the formula for density**:
Density (D) is defined as mass (M) divided by volume (V):
\[ D = \frac{M}{V} \]

2. **Identify the percentage errors**:
- The percentage error in mass (\( \Delta M \)) is given as \( 2\% \).
- The percentage error in volume (\( \Delta V \)) is given as \( 3\% \).

3. **Use the formula for percentage error in division**:
When calculating the percentage error in a quotient (like density), the percentage errors are added:
\[ \text{Percentage error in density} = \text{Percentage error in mass} + \text{Percentage error in volume} \]

4. **Substitute the values**:
\[ \text{Percentage error in density} = 2\% + 3\% \]

5. **Calculate the total percentage error**:
\[ \text{Percentage error in density} = 5\% \]

### Final Answer:
The percentage error in the measurement of the density of the object is \( 5\% \).

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