A dimensionally correct equation _____be a correct equation and a dimensionally incorrect equation ________be incorrect The words (in order) to be filled in the blank spaces are

Options

A. must, must
B. must, may
C. may ,may
D. may, must

Answer

To solve the question, we need to analyze the statements regarding dimensionally correct and incorrect equations.

### Step-by-Step Solution:

1. **Understanding Dimensionally Correct Equations:**
- A dimensionally correct equation is one where both sides of the equation have the same dimensions. This means that the physical quantities involved can be expressed in terms of the same fundamental dimensions (length, mass, time, etc.).
- Example: The formula for the volume of a sphere, \( V = \frac{4}{3} \pi R^3 \), is dimensionally correct because both sides have the dimension of volume (L³).

2. **Possibility of Being Correct or Incorrect:**
- Even if an equation is dimensionally correct, it does not guarantee that the equation is physically correct. For instance, if we modify the volume equation to \( V = 3R^3 \), it remains dimensionally correct (both sides still have dimensions of L³), but it is not the correct formula for the volume of a sphere.
- Therefore, a dimensionally correct equation **may** be a correct equation or it may not be a correct equation.

3. **Understanding Dimensionally Incorrect Equations:**
- A dimensionally incorrect equation is one where the dimensions on the left-hand side (LHS) do not match the dimensions on the right-hand side (RHS).
- Example: If we take the area of a circle, \( A = \pi r^2 \), and incorrectly write it as \( A = \pi R^3 \), the dimensions do not match (L² vs. L³).

4. **Conclusion on Incorrect Equations:**
- Since the dimensions do not match in a dimensionally incorrect equation, it must be incorrect. Therefore, a dimensionally incorrect equation **must** be incorrect.

5. **Final Answer:**
- Filling in the blanks, we conclude that:
- A dimensionally correct equation **may** be a correct equation.
- A dimensionally incorrect equation **must** be incorrect.

### Answer:
The words to be filled in the blank spaces are: **may** and **must**.