The error in the measurement of the length of a simple pendulum is `0.1%` and the error in the time period is `2%`. What is the possible percentage of error in the physical quantity having the dimensional formula `LT^(-2)`?

Options

A. `4.1%`
B. `8.2%`
C. `2.2%`
D. `1.1%`

Explanation

To solve the problem, we need to find the possible percentage error in a physical quantity with the dimensional formula \( LT^{-2} \). The steps are as follows:

### Step 1: Understand the given errors
- The error in the measurement of length (\( L \)) is \( 0.1\% \).
- The error in the measurement of time period (\( T \)) is \( 2\% \).

### Step 2: Identify the physical quantity
The physical quantity we are interested in has the dimensional formula \( LT^{-2} \).

### Step 3: Write the expression for the error
The percentage error in a quantity can be derived from its dimensions. For a quantity \( x \) with the dimensions \( LT^{-2} \), we can express the error as:
\[ \frac{\Delta x}{x} \times 100 = \frac{\Delta L}{L} \times 100 - 2 \times \frac{\Delta T}{T} \times 100 \]

### Step 4: Substitute the given errors
Now, we substitute the given percentage errors into the equation:
- \( \frac{\Delta L}{L} \times 100 = 0.1\% \)
- \( \frac{\Delta T}{T} \times 100 = 2\% \)

### Step 5: Calculate the total error
Substituting these values into the error expression:
\[ \frac{\Delta x}{x} \times 100 = 0.1 + 2 \times 2 \]
\[ \frac{\Delta x}{x} \times 100 = 0.1 + 4 = 4.1\% \]

### Step 6: Conclusion
Thus, the possible percentage error in the physical quantity with the dimensional formula \( LT^{-2} \) is \( 4.1\% \).

### Final Answer
The possible percentage error in the physical quantity is \( 4.1\% \).

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