Statement-1 : Pressure can be subtracted from pressure gradient
Statement-2: Only like quantities can be added or subtracted from each other

Options

A. Statement-1 is true and statement -2 is true
B. Statement -1 is true and statement-2 is false
C. Statement-1 is false and statement -2 is true
D. Statement-1 is false and statement -2 is false

Answer

To solve the given question, we need to analyze both statements provided and determine their validity based on the principles of units and measurements, particularly the principle of homogeneity.

### Step-by-Step Solution:

1. **Understanding Statement-1:**
- Statement-1 claims that "Pressure can be subtracted from pressure gradient."
- Pressure is defined as the force applied per unit area, which has the dimensions of \( [P] = \frac{[F]}{[A]} = \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2} \).
- Pressure gradient, on the other hand, is defined as the change in pressure per unit distance, which has the dimensions of \( [\text{Pressure Gradient}] = \frac{[P]}{[x]} = \frac{ML^{-1}T^{-2}}{L} = ML^{-2}T^{-2} \).

2. **Comparing Dimensions:**
- From the above definitions, we can see that pressure has dimensions of \( ML^{-1}T^{-2} \) and pressure gradient has dimensions of \( ML^{-2}T^{-2} \).
- Since the dimensions of pressure and pressure gradient are not the same, they are not like quantities.

3. **Conclusion for Statement-1:**
- Because pressure and pressure gradient are not like quantities, we cannot subtract one from the other.
- Therefore, Statement-1 is **incorrect**.

4. **Understanding Statement-2:**
- Statement-2 states that "Only like quantities can be added or subtracted from each other."
- This aligns with the principle of homogeneity, which states that for addition or subtraction to be valid, the quantities involved must have the same dimensions.

5. **Conclusion for Statement-2:**
- Since Statement-2 correctly describes the principle of homogeneity, it is **correct**.

6. **Final Answer:**
- Based on the analysis, Statement-1 is incorrect, and Statement-2 is correct. Thus, the correct option is that Statement-2 is true.