If the dimensions of a physical quantity are given by `M^(x) L^(y) T^(z)`, then physical quantity may be

Options

A. acceleration due to gravity, if `x=0, y=1, z=-2`
B. atmospheric pressure, if `x=1, y=1, z=-2`
C. linear momentum, if `x=1, y=1, z=-1`
D. potential energy, if `x=1, y=2, z=-2`

Explanation

To determine which physical quantities correspond to the given dimensions \( M^x L^y T^z \), we will analyze each option step by step.

### Step 1: Analyze the dimensions of acceleration due to gravity
- **Physical Quantity**: Acceleration due to gravity
- **Dimensional Formula**:
\[ [g] = M^0 L^1 T^{-2} \]
- **Comparison**:
- \( x = 0 \)
- \( y = 1 \)
- \( z = -2 \)
- **Conclusion**: This matches the given dimensions, so this option is correct.

### Step 2: Analyze the dimensions of atmospheric pressure
- **Physical Quantity**: Atmospheric pressure
- **Dimensional Formula**:
\[ [P] = M^1 L^2 T^{-2} \]
- **Comparison**:
- \( x = 1 \)
- \( y = 2 \)
- \( z = -2 \)
- **Conclusion**: The given dimensions state \( y = 1 \), which does not match. Therefore, this option is incorrect.

### Step 3: Analyze the dimensions of linear momentum
- **Physical Quantity**: Linear momentum
- **Dimensional Formula**:
\[ [p] = M^1 L^1 T^{-1} \]
- **Comparison**:
- \( x = 1 \)
- \( y = 1 \)
- \( z = -1 \)
- **Conclusion**: This matches the given dimensions, so this option is correct.

### Step 4: Analyze the dimensions of potential energy
- **Physical Quantity**: Potential energy
- **Dimensional Formula**:
\[ [U] = M^1 L^2 T^{-2} \]
- **Comparison**:
- \( x = 1 \)
- \( y = 2 \)
- \( z = -2 \)
- **Conclusion**: This matches the given dimensions, so this option is correct.

### Final Conclusion
Based on the analysis:
- **Correct Options**:
- A (Acceleration due to gravity)
- C (Linear momentum)
- D (Potential energy)
- **Incorrect Option**:
- B (Atmospheric pressure)

### Summary of Results
The physical quantities that correspond to the dimensions \( M^x L^y T^z \) are:
- A: Correct
- B: Incorrect
- C: Correct
- D: Correct