The dimensional formula `ML^(2)T^(-2)` stands for

Options

A. Angular velocity
B. Momentum
C. Heat Energy
D. Coefficient of thermal conductivity

Answer

To determine what the dimensional formula \( ML^2T^{-2} \) represents, we can analyze the options given and their corresponding dimensional formulas step by step.

### Step 1: Understand the Dimensional Formula
The dimensional formula \( ML^2T^{-2} \) consists of:
- \( M \): Mass
- \( L^2 \): Area (since it is length squared)
- \( T^{-2} \): Inverse of time squared

### Step 2: Analyze Each Option
We will check each option provided to see which one matches the dimensional formula \( ML^2T^{-2} \).

#### Option A: Angular Velocity
- **Formula**: Angular velocity \( \omega = \frac{2\pi}{T} \)
- **Dimensional Formula**: \( T^{-1} \)
- **Conclusion**: This does not match \( ML^2T^{-2} \).

#### Option B: Momentum
- **Formula**: Momentum \( p = mv \) (mass times velocity)
- **Dimensional Formula**: \( MLT^{-1} \)
- **Conclusion**: This does not match \( ML^2T^{-2} \).

#### Option C: Heat Energy
- **Relation**: Heat energy is equivalent to work.
- **Work Formula**: Work \( W = F \cdot d \) (force times distance)
- **Force Formula**: \( F = ma \) (mass times acceleration)
- **Dimensional Formula for Force**: \( MLT^{-2} \)
- **Dimensional Formula for Work**:
\[ W = F \cdot d \implies [W] = [F][d] = (MLT^{-2})(L) = ML^2T^{-2} \]
- **Conclusion**: This matches \( ML^2T^{-2} \).

#### Option D: Coefficient of Thermal Conductivity
- **Relation**: \( k = \frac{Q}{t \cdot A \cdot \Delta T / \Delta x} \)
- **Dimensional Analysis**: The dimensional formula involves multiple quantities (heat, time, area, temperature, distance).
- **Conclusion**: This does not simplify to \( ML^2T^{-2} \).

### Final Conclusion
The only option that matches the dimensional formula \( ML^2T^{-2} \) is **Option C: Heat Energy**.

### Summary
The dimensional formula \( ML^2T^{-2} \) stands for **Heat Energy**.

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