A and B are two physical quantities having different dimensions. Then which of the following operation dimensionally correct.

Options

A. ` A+B `
B. `"log" A/B`
C. `A/B`
D. `e^(A//B)`

Explanation

To determine which operation involving two physical quantities A and B with different dimensions is dimensionally correct, we need to analyze each operation step by step.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have two physical quantities, A and B, which have different dimensions. We need to evaluate various operations to see which one is dimensionally correct.

2. **Evaluating the Operations**:
- **Operation 1: A + B**
- When adding two quantities, they must have the same dimensions. Since A and B have different dimensions, this operation is dimensionally incorrect.

- **Operation 2: log(A) + log(B)**
- The logarithm of a quantity is only defined for dimensionless numbers. Since A and B have different dimensions, they cannot be converted into dimensionless numbers simultaneously. Therefore, this operation is also dimensionally incorrect.

- **Operation 3: A / B**
- Division of two quantities with different dimensions is valid. The result will have a new dimension that is a ratio of the dimensions of A and B. Thus, this operation is dimensionally correct.

- **Operation 4: e^(A)**
- The exponential function requires a dimensionless argument. Since A has a dimension, this operation is dimensionally incorrect.

3. **Conclusion**:
- The only dimensionally correct operation among the options given is **Operation 3: A / B**.

### Final Answer:
The dimensionally correct operation is **A / B**.

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