Statement-I: If a physical quantity has a unit, it must not be dimensionless.
Statement-2: A formula derived using dimensional but no unit.

Options

A. Statement-1 is true and statement -2 is true
B. Statement -1 is true and statement-2 is false
C. Statement-1 is false and statement -2 is true
D. Statement-1 is false and statement -2 is false

Answer

To analyze the statements provided in the question, we will break down each statement and evaluate their validity step by step.

### Step 1: Understanding Statement-I
**Statement-I:** If a physical quantity has a unit, it must not be dimensionless.

1. **Definition of Units and Dimensions:**
- A physical quantity can have a unit (like meter, kilogram, etc.) and can also have dimensions (like length, mass, etc.).
- A dimensionless quantity is one that does not have any physical dimensions associated with it (like pure numbers).

2. **Evaluation:**
- The statement suggests that if a quantity has a unit, it cannot be dimensionless. This is incorrect because dimensionless quantities can still have units in certain contexts (e.g., angles measured in radians or percentages).
- Therefore, Statement-I is **false**.

### Step 2: Understanding Statement-II
**Statement-II:** A formula derived using dimensional analysis but no unit.

1. **Dimensional Analysis:**
- Dimensional analysis is a method used to derive relationships between physical quantities based on their dimensions.
- It can help in checking the consistency of equations and deriving formulas.

2. **Evaluation:**
- The statement implies that one can derive a formula using dimensions without involving units. While dimensional analysis does focus on dimensions, it is often used alongside units to ensure that the derived formula is physically meaningful.
- However, it is possible to derive relationships purely based on dimensions without specifying units. For example, the relationship between force, mass, and acceleration can be expressed in terms of dimensions (F = [M][L][T^-2]) without specifying the units.
- Therefore, Statement-II can be considered **true** in a broader sense, but it lacks clarity.

### Conclusion
- **Statement-I:** False
- **Statement-II:** True (but needs clarification)

### Final Answer
Both statements cannot be considered true simultaneously. Statement-I is false, and Statement-II is somewhat misleading but can be considered true in specific contexts.

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