If the dimension of a physical quantity are given by `M^a L^b T^c,` then the physical quantity will be

Options

A. force, if `a=0, b=-1, c=-2`
B. pressure if `a=1, b=-1 , c=-2`
C. velocity if `a=1, b=0, c=-1`
D. acceleration if `a=1, b=1, c=-2`

Answer

To solve the problem, we need to analyze the given dimensions \( M^a L^b T^c \) and compare them with the dimensional formulas of the physical quantities provided in the options.

### Step-by-Step Solution:

1. **Identify the Dimensional Formula for Each Quantity**:
- **Force**:
- Force is defined as mass times acceleration.
- The dimensional formula for mass is \( M \).
- The dimensional formula for acceleration is \( L T^{-2} \).
- Therefore, the dimensional formula for force is:
\[ [F] = M \cdot (L T^{-2}) = M^1 L^1 T^{-2} \quad \Rightarrow \quad a = 1, b = 1, c = -2 \]

- **Pressure**:
- Pressure is defined as force per unit area.
- The dimensional formula for area is \( L^2 \).
- Therefore, the dimensional formula for pressure is:
\[ [P] = \frac{[F]}{[A]} = \frac{M^1 L^1 T^{-2}}{L^2} = M^1 L^{-1} T^{-2} \quad \Rightarrow \quad a = 1, b = -1, c = -2 \]

- **Velocity**:
- Velocity is defined as displacement per unit time.
- The dimensional formula for displacement is \( L \) and for time is \( T \).
- Therefore, the dimensional formula for velocity is:
\[ [V] = \frac{L}{T} = L^1 T^{-1} \quad \Rightarrow \quad a = 0, b = 1, c = -1 \]

- **Acceleration**:
- Acceleration is defined as change in velocity per unit time.
- Therefore, the dimensional formula for acceleration is:
\[ [A] = \frac{L}{T^2} = L^1 T^{-2} \quad \Rightarrow \quad a = 0, b = 1, c = -2 \]

2. **Compare Dimensions**:
- Now we compare the dimensions \( M^a L^b T^c \) with the derived formulas for each physical quantity:
- For **Force**: \( a = 1, b = 1, c = -2 \) (not matching)
- For **Pressure**: \( a = 1, b = -1, c = -2 \) (matches)
- For **Velocity**: \( a = 0, b = 1, c = -1 \) (not matching)
- For **Acceleration**: \( a = 0, b = 1, c = -2 \) (not matching)

3. **Conclusion**:
- The only option that matches the dimensions \( M^a L^b T^c \) where \( a = 1, b = -1, c = -2 \) is **Pressure**.

### Final Answer:
The physical quantity represented by the dimensions \( M^a L^b T^c \) is **Pressure** if \( a = 1, b = -1, c = -2 \).