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

Answer

To determine the physical quantity that corresponds to the dimensions \( M^{1}L^{-1}T^{-2} \), we can follow these steps:

### Step 1: Analyze the Dimensions
The given dimensions are:
- \( M^{1} \): This indicates that the quantity has a mass component.
- \( L^{-1} \): This indicates that the quantity has an inverse length component.
- \( T^{-2} \): This indicates that the quantity has an inverse time squared component.

### Step 2: Identify Possible Quantities
We need to find a physical quantity that has these dimensions. A good starting point is to consider common physical quantities that involve mass, length, and time.

### Step 3: Consider Stress and Pressure
One of the most relevant physical quantities that comes to mind is pressure (or stress), which is defined as force per unit area.

### Step 4: Relate Pressure to the Given Dimensions
1. **Force** has dimensions of \( M^{1}L^{1}T^{-2} \) (from Newton's second law, \( F = ma \)).
2. **Area** has dimensions of \( L^{2} \).

Thus, pressure \( P \) can be expressed as:
\[ P = \frac{F}{A} \]
Substituting the dimensions of force and area:
\[ P = \frac{M^{1}L^{1}T^{-2}}{L^{2}} = M^{1}L^{-1}T^{-2} \]

### Step 5: Conclusion
The dimensions \( M^{1}L^{-1}T^{-2} \) correspond to the physical quantity of **pressure** or **stress**.

### Final Answer
The quantity for which the dimensions \( M^{1}L^{-1}T^{-2} \) are applicable is **pressure** (or **stress**).

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