Give the quantities for which the following are the dimensions:
`M^(1)L^(2)`

Answer

To find the physical quantity that has the dimensions \( M^1 L^2 \), we can follow these steps:

### Step 1: Understand the Dimensions
The dimensions \( M^1 L^2 \) indicate that the quantity has a mass dimension of 1 (which means it is proportional to mass) and a length dimension of 2 (which means it is proportional to the square of a length).

### Step 2: Identify Possible Quantities
We need to think of physical quantities that can be expressed in terms of mass and length. One common quantity that fits this description is the moment of inertia.

### Step 3: Recall the Formula for Moment of Inertia
The moment of inertia \( I \) of a body is defined as:
\[ I = m \cdot k^2 \]
where \( m \) is the mass of the body and \( k \) is the radius of gyration.

### Step 4: Determine the Dimensions of Moment of Inertia
In the formula for moment of inertia:
- The dimension of mass \( m \) is \( M^1 \).
- The radius of gyration \( k \) has dimensions of length \( L \), and since it is squared in the formula, its dimensions become \( L^2 \).

Thus, the dimensions of moment of inertia can be expressed as:
\[ I = m \cdot k^2 \implies [I] = M^1 \cdot L^2 = M^1 L^2 \]

### Step 5: Conclusion
Therefore, the physical quantity that has the dimensions \( M^1 L^2 \) is the **moment of inertia**.

---