The dimensions of surface tension are

Options

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

Answer

To find the dimensions of surface tension, we can follow these steps:

### Step 1: Understand the definition of surface tension
Surface tension is defined as the force acting per unit length along the surface of a liquid. Mathematically, it can be expressed as:
\[ \text{Surface Tension} = \frac{\text{Force}}{\text{Length}} \]

### Step 2: Write the dimensional formula for force
The dimensional formula for force (F) is derived from Newton's second law, which states that force is equal to mass times acceleration. The dimensional formula for mass (M) is \(M\) and for acceleration (a) is \(LT^{-2}\). Therefore, the dimensional formula for force is:
\[ [F] = [M][a] = M \cdot (LT^{-2}) = MLT^{-2} \]

### Step 3: Write the dimensional formula for length
The dimensional formula for length (L) is simply:
\[ [L] = L \]

### Step 4: Substitute the dimensional formulas into the surface tension equation
Now we can substitute the dimensional formula for force and length into the surface tension equation:
\[ [\text{Surface Tension}] = \frac{[F]}{[L]} = \frac{MLT^{-2}}{L} \]

### Step 5: Simplify the expression
When we divide \(MLT^{-2}\) by \(L\), the \(L\) in the numerator and denominator cancels out:
\[ [\text{Surface Tension}] = MT^{-2} \]

### Conclusion
Thus, the dimensions of surface tension are:
\[ \text{Surface Tension} = MT^{-2} \]

### Final Answer
The correct option for the dimensions of surface tension is \(MT^{-2}\).

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