The dimensional formula for angular momentum is

Options

A. `[ML^(0)L^(2)T^(-2)]`
B. `[ML^(2)T^(-1)]`
C. `[MLT^(-1)]`
D. `[ML^(2)T^(-2)]`

Explanation

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

### Step 1: Understand the Definition of Angular Momentum
Angular momentum (L) is defined as the cross product of the position vector (R) and the momentum (P) of an object. Mathematically, it can be expressed as:
\[ L = R \times P \]

### Step 2: Identify the Dimensions of Position Vector (R)
The position vector (R) represents a distance from the axis of rotation to the point of interest. Therefore, its dimension is:
\[ [R] = L \]
where \( L \) stands for length.

### Step 3: Identify the Dimensions of Momentum (P)
Momentum (P) is defined as the product of mass (m) and velocity (v). The formula for momentum is:
\[ P = m \cdot v \]
The dimensions of mass (m) are:
\[ [m] = M \]
The dimensions of velocity (v) are given by:
\[ [v] = \frac{L}{T} \]
where \( T \) stands for time. Therefore, the dimensions of momentum are:
\[ [P] = [m] \cdot [v] = M \cdot \frac{L}{T} = M L T^{-1} \]

### Step 4: Combine the Dimensions to Find Angular Momentum
Now that we have the dimensions for both R and P, we can substitute them into the equation for angular momentum:
\[ [L] = [R] \times [P] = L \times (M L T^{-1}) \]
This simplifies to:
\[ [L] = M L^2 T^{-1} \]

### Step 5: Write the Final Dimensional Formula
Thus, the dimensional formula for angular momentum is:
\[ [L] = M L^2 T^{-1} \]

### Final Answer
The dimensional formula for angular momentum is:
\[ M L^2 T^{-1} \]

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