STATEMENT-1 A dimensionless quantity may have a unit
STATEMENT-2 A constant may not be unitless.

Options

A. Statement-1 is True , Statement-2 is True ,Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True , Statement-2 is True ,Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True , Statement-2 is False
D. Statement-1 is False, Statement-2 is True

Answer

To analyze the statements provided, we will break down each statement and provide a clear explanation for both.

### Step-by-Step Solution:

**Step 1: Analyze Statement 1**
- Statement 1 claims that a dimensionless quantity may have a unit.
- A dimensionless quantity is defined as a quantity that has no physical dimensions and is represented by a dimension of \(L^0 M^0 T^0\).
- An example of a dimensionless quantity is angular displacement, which can be expressed in radians.
- Radians are derived from the ratio of two lengths (arc length to radius), where both lengths are measured in meters. Hence, the units cancel out, making it dimensionless. However, it still has a unit (radian).
- Therefore, Statement 1 is **True**.

**Step 2: Analyze Statement 2**
- Statement 2 claims that a constant may not be unitless.
- A constant in physics often has units associated with it. For example, in Hooke's Law, the restoring force \(F\) is proportional to the displacement \(x\) from the mean position, represented as \(F = -kx\).
- Here, \(k\) is the spring constant, which has units of Newtons per meter (N/m). This clearly shows that \(k\) is not unitless.
- Therefore, Statement 2 is also **True**.

**Step 3: Determine the Relationship Between the Statements**
- While both statements are true, Statement 2 does not adequately explain Statement 1.
- Statement 1 discusses the nature of dimensionless quantities, while Statement 2 discusses the nature of constants. They are related but do not directly explain each other.
- Thus, the conclusion is that both statements are true, but Statement 2 is not a correct explanation of Statement 1.

### Final Conclusion:
- **Statement 1**: True
- **Statement 2**: True
- **Explanation Relationship**: Statement 2 does not correctly explain Statement 1.