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

Options

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

Answer

To find out what the dimensional formula `[ML^(-1)T^(-2)]` corresponds to, we can analyze various physical quantities and their dimensional formulas step by step.

### Step-by-Step Solution:

1. **Understanding the Dimensional Formula**:
The given dimensional formula is `[ML^(-1)T^(-2)]`. This indicates that the quantity has dimensions of mass (M), inverse length (L^(-1)), and inverse time squared (T^(-2)).

2. **Analyzing Common Physical Quantities**:
We will check the dimensional formulas of various physical quantities to see which one matches `[ML^(-1)T^(-2)]`.

3. **Checking Force**:
- The formula for force is given by \( F = m \cdot a \), where \( m \) is mass and \( a \) is acceleration.
- The dimensional formula for mass \( m \) is \( [M] \).
- The dimensional formula for acceleration \( a \) is \( [L T^{-2}] \).
- Therefore, the dimensional formula for force is:
\[ [F] = [M][L T^{-2}] = [ML T^{-2}] \]
- This does not match our given formula.

4. **Checking Coefficient of Friction**:
- The coefficient of friction \( \mu \) is a dimensionless quantity, so it does not have a dimensional formula.

5. **Checking Modulus of Elasticity**:
- The modulus of elasticity (or modulus of rigidity) is defined as stress over strain.
- Stress is defined as force per unit area, which has the dimensional formula:
\[ [\text{Stress}] = \frac{[F]}{[L^2]} = \frac{[ML T^{-2}]}{[L^2]} = [ML^{-1}T^{-2}] \]
- Strain is dimensionless, so the modulus of elasticity has the same dimensions as stress, which is:
\[ [\text{Modulus of Elasticity}] = [ML^{-1}T^{-2}] \]
- This matches our given formula.

6. **Conclusion**:
- The dimensional formula `[ML^(-1)T^(-2)]` corresponds to the **Modulus of Elasticity**.

### Final Answer:
The dimensional formula `[ML^(-1)T^(-2)]` corresponds to the **Modulus of Elasticity**.

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