A : All physically correct equations are dimensionally correct.
R : All dimensionally correct equations are physically correct.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statements, then mark (4).

Answer

To solve the question, we need to analyze the two statements given:

**Assertion (A):** All physically correct equations are dimensionally correct.
**Reason (R):** All dimensionally correct equations are physically correct.

### Step 1: Analyze the Assertion (A)

1. **Understanding the Assertion:**
- The assertion states that if an equation is physically correct, it must also be dimensionally correct.

2. **Example Verification:**
- Consider the kinematic equation: \( v - u = a \cdot t \).
- Here, \( v \) and \( u \) are velocities (units: m/s), \( a \) is acceleration (units: m/s²), and \( t \) is time (units: s).
- The left side (velocity difference) has units of m/s, and the right side (acceleration multiplied by time) also results in m/s.
- Since both sides have the same dimensions, this equation is dimensionally correct.

3. **Conclusion for Assertion:**
- Since we can find examples where physically correct equations are dimensionally correct, the assertion is **true**.

### Step 2: Analyze the Reason (R)

1. **Understanding the Reason:**
- The reason states that if an equation is dimensionally correct, it must also be physically correct.

2. **Example Verification:**
- Consider the equation for the time period of a simple pendulum:
\[ T = 2\pi \sqrt{\frac{l}{g}} \]
- This is a physically correct equation where \( T \) is time, \( l \) is length, and \( g \) is acceleration due to gravity.
- If we ignore the constant \( 2\pi \) and write \( T = \sqrt{\frac{l}{g}} \), we can check its dimensional correctness:
- Dimensions of \( l \) are [L], and dimensions of \( g \) are [L][T]⁻².
- Thus, \( \frac{l}{g} \) has dimensions of [T]², and taking the square root gives dimensions of [T].
- Therefore, \( T = \sqrt{\frac{l}{g}} \) is dimensionally correct but not physically correct because it lacks the constant \( 2\pi \).

3. **Conclusion for Reason:**
- Since we found an example where a dimensionally correct equation is not physically correct, the reason is **false**.

### Final Conclusion

- The assertion (A) is **true**, and the reason (R) is **false**.
- Therefore, the correct option is that the assertion is true and the reason is false.