Dimensional formula for strain is

Options

A. `[M^(0)LT^(-2)]`
B. [MLT]
C. `[M^(2)LT^(-2)]`
D. `[M^(0)L^(0)T^(0)]`

Answer

To find the dimensional formula for strain, we can follow these steps:

### Step 1: Understand the definition of strain
Strain is defined as the ratio of the change in length (ΔL) to the original length (L). Mathematically, it can be expressed as:
\[ \text{Strain} = \frac{\Delta L}{L} \]

### Step 2: Identify the dimensions of the quantities involved
1. **Change in Length (ΔL)**: The change in length is measured in units of length. Therefore, its dimensional formula is:
\[ [\Delta L] = L \]

2. **Original Length (L)**: The original length is also measured in units of length, so its dimensional formula is:
\[ [L] = L \]

### Step 3: Substitute the dimensional formulas into the strain formula
Now, substituting the dimensions of ΔL and L into the strain formula:
\[ \text{Strain} = \frac{[\Delta L]}{[L]} = \frac{L}{L} \]

### Step 4: Simplify the expression
When we simplify the expression:
\[ \text{Strain} = 1 \]
This indicates that strain is a dimensionless quantity, which means it has no physical dimensions.

### Step 5: Write the dimensional formula for strain
Since strain is dimensionless, we can express its dimensional formula as:
\[ [\text{Strain}] = M^0 L^0 T^0 \]

### Final Answer
Thus, the dimensional formula for strain is:
\[ M^0 L^0 T^0 \]