(A) The correctness of an equation is verified using the principle of homogeneity
(B) All unit less quantities are dimensional less.

Options

A. Both A & B are true
B. Both A & B are false
C. Only A is true
D. Only B is true

Answer

To solve the question regarding the correctness of the statements (A) and (B), we will analyze each statement step by step.

### Step-by-Step Solution:

**Step 1: Analyze Statement A**
- Statement A claims that "The correctness of an equation is verified using the principle of homogeneity."
- The principle of homogeneity states that for an equation to be physically meaningful, the dimensions of all terms on both sides of the equation must be the same.
- For example, consider the equation for force: \( F = m \cdot a \).
- The dimensional formula for force \( F \) is \( [M^1 L^1 T^{-2}] \).
- The dimensional formula for mass \( m \) is \( [M^1] \) and for acceleration \( a \) is \( [L^1 T^{-2}] \).
- Therefore, \( [M^1] \cdot [L^1 T^{-2}] = [M^1 L^1 T^{-2}] \), which confirms that both sides of the equation have the same dimensions.
- Thus, Statement A is **true**.

**Step 2: Analyze Statement B**
- Statement B claims that "All unitless quantities are dimensionless."
- A unitless quantity is one that does not have any physical units associated with it. For example, strain, which is the ratio of change in length to original length, is unitless because it can be expressed as \( \frac{L}{L} \) (length over length).
- Since the units cancel out, the dimension of strain is \( [L^1]/[L^1] = [L^0] \), which means it is dimensionless.
- Therefore, Statement B is also **true**.

**Step 3: Conclusion**
- Since both statements A and B have been verified to be true, the correct answer is that both A and B are true.

### Final Answer:
Both A and B are true.

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