Assertion: Pressure can not be subtracted from pressure gradient.
Reason: Pressure and pressure gradient have different dimensions.

Options

A. if both assertion and reason are true reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation fo assertion.
C. If assertion is true but reaso is false.
D. IF both assertion and reason are false.

Explanation

To solve the question, we need to analyze the assertion and the reason provided regarding pressure and pressure gradient.

**Step 1: Understand the Assertion**
The assertion states that pressure cannot be subtracted from pressure gradient. This implies that these two quantities are not compatible for arithmetic operations like subtraction.

**Step 2: Understand the Reason**
The reason provided is that pressure and pressure gradient have different dimensions. This is a crucial point because in physics, only quantities with the same dimensions can be added or subtracted.

**Step 3: Calculate the Dimensions of Pressure**
Pressure (P) is defined as force (F) per unit area (A). The formula for pressure is:
\[ P = \frac{F}{A} \]
The dimensions of force (F) are given by:
\[ F = m \cdot a = m \cdot \frac{l}{t^2} \]
Thus, the dimensions of force are:
\[ [F] = [M^1 L^1 T^{-2}] \]
The dimensions of area (A) are:
\[ [A] = L^2 \]
Now, substituting these into the pressure formula:
\[ [P] = \frac{[F]}{[A]} = \frac{[M^1 L^1 T^{-2}]}{[L^2]} = [M^1 L^{-1} T^{-2}] \]

**Step 4: Calculate the Dimensions of Pressure Gradient**
Pressure gradient (∇P) is defined as the change in pressure per unit distance. The formula for pressure gradient is:
\[ \nabla P = \frac{P}{d} \]
where \( d \) is distance. The dimensions of distance are:
\[ [d] = L^1 \]
Now substituting the dimensions of pressure:
\[ [\nabla P] = \frac{[P]}{[d]} = \frac{[M^1 L^{-1} T^{-2}]}{[L^1]} = [M^1 L^{-2} T^{-2}] \]

**Step 5: Compare the Dimensions**
Now we have:
- Dimensions of Pressure: \([M^1 L^{-1} T^{-2}]\)
- Dimensions of Pressure Gradient: \([M^1 L^{-2} T^{-2}]\)

Since the dimensions are different, this confirms that pressure cannot be subtracted from pressure gradient.

**Step 6: Conclusion**
Both the assertion and the reason are correct. The assertion is true because pressure and pressure gradient have different dimensions, which makes them incompatible for subtraction. The reason correctly explains the assertion.

Thus, the answer is that both the assertion and reason are true, and the reason is the correct explanation of the assertion.

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