Two cubical boxes X and Y are made up of different materials, but they have equal mass. Surface areas of boxes X and Y are `10 m^2` and `15 m^2` respectively. If `P_X` and `P_Y` are the pressure exerted by boxes X and Y on a plane surface respectively, then

Options

A. `P_X gt P_Y`
B. `P_X lt P_Y`
C. `P_X = P_Y`
D. `P_X = P_Y=0`

Answer

To solve the problem, we need to determine the relationship between the pressures exerted by the two cubical boxes X and Y on a plane surface.

### Step-by-Step Solution:

1. **Understanding Pressure**:
Pressure (P) is defined as the force (F) applied per unit area (A). Mathematically, it is expressed as:
\[ P = \frac{F}{A} \]

2. **Identifying the Force**:
In this case, the force exerted by each box on the surface is equal to its weight. Since both boxes have equal mass (m), the weight (W) of each box can be expressed as:
\[ W = m \cdot g \]
where \( g \) is the acceleration due to gravity.

3. **Calculating Pressure for Box X**:
For box X, with surface area \( A_X = 10 \, m^2 \), the pressure \( P_X \) can be calculated as:
\[ P_X = \frac{W_X}{A_X} = \frac{m \cdot g}{10} \]

4. **Calculating Pressure for Box Y**:
For box Y, with surface area \( A_Y = 15 \, m^2 \), the pressure \( P_Y \) can be calculated as:
\[ P_Y = \frac{W_Y}{A_Y} = \frac{m \cdot g}{15} \]

5. **Comparing Pressures**:
Since both boxes have the same weight (force), we can compare the pressures:
\[ P_X = \frac{m \cdot g}{10} \quad \text{and} \quad P_Y = \frac{m \cdot g}{15} \]
To compare \( P_X \) and \( P_Y \), we can observe that:
\[ P_X = \frac{m \cdot g}{10} > P_Y = \frac{m \cdot g}{15} \]
This is because \( \frac{1}{10} > \frac{1}{15} \).

6. **Conclusion**:
Therefore, the pressure exerted by box X is greater than the pressure exerted by box Y:
\[ P_X > P_Y \]

### Final Answer:
The pressure exerted by box X is greater than the pressure exerted by box Y, i.e., \( P_X > P_Y \).