The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate by using the formula `p=(F)/(l^(2))`. If the maximum errors in the measurment of force and length are `4%` and `2%` respectively. Then the maximum error in the measurment of pressure is

Options

A. 0.01
B. 0.02
C. 0.08
D. 0.1

Answer

To solve the problem, we need to determine the maximum error in the measurement of pressure \( P \) given the formula:

\[ P = \frac{F}{L^2} \]

where \( F \) is the force applied on the plate and \( L \) is the length of the sides of the square plate.

### Step 1: Identify the errors in measurements
- The maximum error in the measurement of force \( F \) is given as \( 4\% \).
- The maximum error in the measurement of length \( L \) is given as \( 2\% \).

### Step 2: Convert percentage errors to fractional errors
- The fractional error in force \( \delta F/F \) is:
\[ \frac{\delta F}{F} = \frac{4}{100} = 0.04 \]

- The fractional error in length \( \delta L/L \) is:
\[ \frac{\delta L}{L} = \frac{2}{100} = 0.02 \]

### Step 3: Relate the errors to pressure
Using the formula for pressure, we can express the fractional error in pressure \( \delta P/P \) as follows:
\[ \frac{\delta P}{P} = \frac{\delta F}{F} + 2 \frac{\delta L}{L} \]

### Step 4: Substitute the fractional errors into the equation
Now, substituting the values we have:
\[ \frac{\delta P}{P} = 0.04 + 2 \times 0.02 \]

### Step 5: Calculate the total fractional error
Calculating the right-hand side:
\[ \frac{\delta P}{P} = 0.04 + 0.04 = 0.08 \]

### Step 6: Convert the fractional error to percentage
To convert the fractional error to a percentage, we multiply by 100:
\[ \text{Maximum error in pressure} = 0.08 \times 100 = 8\% \]

### Final Answer
The maximum error in the measurement of pressure is \( 8\% \).

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