The dimensions of (angular momentum)/(magnetic moment) are

Options

A. `[M^(3)LT^(-2)A^(2)]`
B. `[MA^(-1)T^(-1)]`
C. `[ML^(2)A^(-2)T]`
D. `[M^(2)L^(-3)AT^(2)]`

Answer

To find the dimensions of the ratio of angular momentum to magnetic moment, we will follow these steps:

### Step 1: Determine the dimensions of angular momentum
Angular momentum (L) is defined as the product of the moment of inertia and angular velocity. The moment of inertia has dimensions of mass times length squared (ML²), and angular velocity has dimensions of time inverse (T⁻¹). Therefore, the dimensions of angular momentum can be expressed as:

\[ \text{Dimensions of Angular Momentum} = [L] = [M][L^2][T^{-1}] = M L^2 T^{-1} \]

### Step 2: Determine the dimensions of magnetic moment
The magnetic moment (M) is defined as the product of current (I) and area (A). The dimensions of current are denoted as [A] (Ampere), and the area has dimensions of length squared (L²). Thus, the dimensions of magnetic moment can be expressed as:

\[ \text{Dimensions of Magnetic Moment} = [M] = [A][L^2] = A L^2 \]

### Step 3: Divide the dimensions of angular momentum by the dimensions of magnetic moment
Now we can find the dimensions of the ratio of angular momentum to magnetic moment:

\[ \frac{\text{Dimensions of Angular Momentum}}{\text{Dimensions of Magnetic Moment}} = \frac{M L^2 T^{-1}}{A L^2} \]

### Step 4: Simplify the expression
When we divide, the \(L^2\) terms cancel out:

\[ \frac{M L^2 T^{-1}}{A L^2} = \frac{M}{A} T^{-1} \]

This can be expressed in dimensional notation as:

\[ \text{Dimensions} = M A^{-1} T^{-1} \]

### Final Answer
Thus, the dimensions of angular momentum divided by magnetic moment are:

\[ M A^{-1} T^{-1} \]