The dimensional formula of physical quantity is `[M^(a)L^(b)T^(c)]`.Then that physical quantity is

Options

A. A. surface tension if a=1,b=1,c=-2
B. B. force if a=1,b=1,c=2
C. C. angular frequency if a=0,b=0,c=-1
D. D. spring constant if a=1,b=-1,c=-2

Explanation

To determine which physical quantity corresponds to the given dimensional formula \([M^a L^b T^c]\), we will analyze each option provided based on their dimensional formulas.

### Step 1: Understand the given dimensional formula
The dimensional formula is given as \([M^a L^b T^c]\), where:
- \(M\) represents mass,
- \(L\) represents length,
- \(T\) represents time.

### Step 2: Analyze each option

#### Option A: Surface Tension
- **Unit**: Newton per meter (N/m)
- **Dimensional formula**:
\[ \text{Newton} = \text{kg} \cdot \text{m/s}^2 = M^1 L^1 T^{-2} \]
Therefore, surface tension:
\[ \text{Surface Tension} = \frac{M^1 L^1 T^{-2}}{L^1} = M^1 L^0 T^{-2} \]
This gives us \(a = 1\), \(b = 0\), \(c = -2\).

#### Option B: Force
- **Unit**: Newton (N)
- **Dimensional formula**:
\[ \text{Newton} = \text{kg} \cdot \text{m/s}^2 = M^1 L^1 T^{-2} \]
Here, we have \(a = 1\), \(b = 1\), \(c = -2\).

#### Option C: Angular Frequency
- **Unit**: Radians per second (1/s)
- **Dimensional formula**:
\[ \text{Angular Frequency} = \frac{1}{T} = M^0 L^0 T^{-1} \]
Thus, \(a = 0\), \(b = 0\), \(c = -1\).

#### Option D: Spring Constant
- **Unit**: Newton per meter (N/m)
- **Dimensional formula**:
\[ \text{Spring Constant} = \frac{\text{Force}}{\text{Length}} = \frac{M^1 L^1 T^{-2}}{L^1} = M^1 L^0 T^{-2} \]
This gives us \(a = 1\), \(b = 0\), \(c = -2\).

### Step 3: Compare with the options
Now let's compare the results with the options provided:
- **Option A**: \(a = 1\), \(b = 0\), \(c = -2\) (Incorrect)
- **Option B**: \(a = 1\), \(b = 1\), \(c = -2\) (Incorrect)
- **Option C**: \(a = 0\), \(b = 0\), \(c = -1\) (Correct)
- **Option D**: \(a = 1\), \(b = 0\), \(c = -2\) (Incorrect)

### Conclusion
The correct answer is **Option C: Angular Frequency**, which has the dimensional formula \(M^0 L^0 T^{-1}\).