The surface area of the base of a brick X is `100 cm^(2)`. The surface area of the base of the brick Y is `250 cm^(2)`. Each brick weighs 100 N. Which of the following is correct if `P_(1)` and `P_(2)` are the pressures exerted by the bricks X and Y respectively?

Options

A. `P_(1) = P_(2)`
B. `P_(1) gt P_(2)`
C. `P_(1) lt P_(2)`
D. `P_(1) = P_(2) = 0`

Answer

To solve the problem, we need to calculate the pressure exerted by each brick using the formula for pressure:

\[ P = \frac{F}{A} \]

where:
- \( P \) is the pressure,
- \( F \) is the force (weight of the brick in this case), and
- \( A \) is the area of the base.

### Step 1: Calculate the pressure exerted by brick X (\( P_1 \))

Given:
- Weight of brick X, \( F_1 = 100 \, N \)
- Surface area of the base of brick X, \( A_1 = 100 \, cm^2 \)

Convert the area from \( cm^2 \) to \( m^2 \) for standard SI units:
\[ A_1 = 100 \, cm^2 = 100 \times 10^{-4} \, m^2 = 0.01 \, m^2 \]

Now, calculate \( P_1 \):
\[ P_1 = \frac{F_1}{A_1} = \frac{100 \, N}{0.01 \, m^2} = 10000 \, N/m^2 \]

### Step 2: Calculate the pressure exerted by brick Y (\( P_2 \))

Given:
- Weight of brick Y, \( F_2 = 100 \, N \)
- Surface area of the base of brick Y, \( A_2 = 250 \, cm^2 \)

Convert the area from \( cm^2 \) to \( m^2 \):
\[ A_2 = 250 \, cm^2 = 250 \times 10^{-4} \, m^2 = 0.025 \, m^2 \]

Now, calculate \( P_2 \):
\[ P_2 = \frac{F_2}{A_2} = \frac{100 \, N}{0.025 \, m^2} = 4000 \, N/m^2 \]

### Step 3: Compare the pressures \( P_1 \) and \( P_2 \)

Now we have:
- \( P_1 = 10000 \, N/m^2 \)
- \( P_2 = 4000 \, N/m^2 \)

Since \( P_1 > P_2 \), we conclude:
\[ P_1 \text{ is greater than } P_2 \]

### Final Answer:
The pressure exerted by brick X is greater than the pressure exerted by brick Y, i.e., \( P_1 > P_2 \).

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