If `L = (2 pm 0.01) m and B = (1 pm 0.02)m` then L/B is

Options

A. `(2 +- 0.03)m`
B. `(2 +- 0.015)m`
C. `(2 +- 0.01)m`
D. `(2 +- 0.05)m`

Answer

To solve the problem of finding \( \frac{L}{B} \) where \( L = (2 \pm 0.01) \, m \) and \( B = (1 \pm 0.02) \, m \), we will follow these steps:

### Step 1: Identify the values and uncertainties
We have:
- \( L = 2 \, m \) with an uncertainty \( \Delta L = 0.01 \, m \)
- \( B = 1 \, m \) with an uncertainty \( \Delta B = 0.02 \, m \)

### Step 2: Calculate the value of \( \frac{L}{B} \)
The value of \( \frac{L}{B} \) is calculated as follows:
\[ \frac{L}{B} = \frac{2 \, m}{1 \, m} = 2 \]

### Step 3: Calculate the uncertainty in \( \frac{L}{B} \)
To find the uncertainty in the division, we use the formula for the propagation of uncertainty:
\[ \frac{\Delta x}{x} = \frac{\Delta L}{L} + \frac{\Delta B}{B} \]
where \( x = \frac{L}{B} \).

### Step 4: Substitute the values into the uncertainty formula
Substituting the known values:
\[ \Delta x = x \left( \frac{\Delta L}{L} + \frac{\Delta B}{B} \right) \]
Substituting the values:
\[ \Delta x = 2 \left( \frac{0.01}{2} + \frac{0.02}{1} \right) \]

### Step 5: Calculate the individual terms
Calculating each term:
\[ \frac{\Delta L}{L} = \frac{0.01}{2} = 0.005 \]
\[ \frac{\Delta B}{B} = \frac{0.02}{1} = 0.02 \]

### Step 6: Add the uncertainties
Now, add the uncertainties:
\[ \Delta x = 2 \left( 0.005 + 0.02 \right) = 2 \times 0.025 = 0.05 \]

### Step 7: Write the final result
Thus, we can express \( \frac{L}{B} \) with its uncertainty:
\[ \frac{L}{B} = 2 \pm 0.05 \]

### Final Answer
\[ \frac{L}{B} = 2 \pm 0.05 \]

---