Assertion Stress and modulus of elasticity have the same dimensions
Reason Strain is dimensionless.

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If both Assertion and Reason are false.

Answer

To determine the validity of the assertion and reason provided in the question, we will analyze both statements step by step.

### Step 1: Understanding Stress
Stress is defined as the force applied per unit area. Mathematically, it can be expressed as:

\[ \text{Stress} = \frac{\text{Force}}{\text{Area}} \]

### Step 2: Dimensions of Stress
The dimension of force (F) is given by:

\[ \text{Force} = \text{mass} \times \text{acceleration} = MLT^{-2} \]

The dimension of area (A) is:

\[ \text{Area} = L^2 \]

Thus, the dimension of stress can be calculated as:

\[ \text{Dimension of Stress} = \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2} \]

### Step 3: Understanding Modulus of Elasticity
The modulus of elasticity (E), specifically Young's modulus, is defined as the ratio of stress to strain:

\[ E = \frac{\text{Stress}}{\text{Strain}} \]

### Step 4: Dimensions of Modulus of Elasticity
Since strain is defined as the change in length divided by the original length, it is a dimensionless quantity. Therefore, the dimension of strain is:

\[ \text{Dimension of Strain} = 0 \quad (\text{dimensionless}) \]

Thus, the dimension of modulus of elasticity can be simplified as:

\[ \text{Dimension of Modulus of Elasticity} = \frac{\text{Dimension of Stress}}{\text{Dimension of Strain}} = \frac{ML^{-1}T^{-2}}{1} = ML^{-1}T^{-2} \]

### Step 5: Conclusion on Assertion and Reason
From the above steps, we can conclude that:

- The dimension of stress is \(ML^{-1}T^{-2}\).
- The dimension of modulus of elasticity is also \(ML^{-1}T^{-2}\).
- Strain is indeed dimensionless.

Thus, both the assertion (that stress and modulus of elasticity have the same dimensions) and the reason (that strain is dimensionless) are true. Furthermore, the reason provides a correct explanation for the assertion.

### Final Answer
Both the assertion and the reason are true, and the reason is the correct explanation of the assertion.

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