`[ML^(-1)T^(-2)]` is the dimensional formula of

Options

A. force
B. coefficient of friction
C. modulus of elasticity
D. energy

Answer

To determine what the dimensional formula `[ML^(-1)T^(-2)]` represents, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given dimensional formula**:
We start with the dimensional formula provided, which is `[ML^(-1)T^(-2)]`.

2. **Interpret the dimensions**:
- `M` represents mass.
- `L` represents length.
- `T` represents time.
- The negative exponent indicates that length is in the denominator.

3. **Convert the dimensional formula to units**:
The dimensional formula can be interpreted in terms of units:
- `[ML^(-1)T^(-2)]` can be rewritten as `kg * m^(-1) * s^(-2)`, which translates to `kg/m/s^2`.

4. **Recognize the physical quantity**:
- The unit `kg/m/s^2` can be recognized as the unit of force per unit area.
- Force is measured in Newtons (N), where 1 N = 1 kg·m/s².
- Therefore, `kg/m/s^2` can be expressed as `N/m²`.

5. **Identify the physical meaning**:
- The unit `N/m²` is defined as Pascal (Pa), which is the SI unit of pressure.
- Hence, the dimensional formula `[ML^(-1)T^(-2)]` represents pressure.

6. **Consider other possibilities**:
- The dimensional formula can also represent the modulus of elasticity since modulus of elasticity is defined as stress (force per unit area) over strain (which is dimensionless).
- Since stress has the same dimensions as pressure, `[ML^(-1)T^(-2)]` can also represent the modulus of elasticity.

### Conclusion:
The dimensional formula `[ML^(-1)T^(-2)]` represents both pressure and modulus of elasticity.

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