Which of the following do not have same dimensions ?

Options

A. Force, surface tension
B. Angle, shear strain
C. Pressure, stress
D. Planck,s constant, angular momentum

Answer

To solve the question of which of the following do not have the same dimensions, we will analyze the dimensions of each option provided.

### Step-by-Step Solution:

1. **Identify the Options**:
Let's assume the options are:
- A) Force
- B) Surface Tension
- C) Angle
- D) Pressure
- E) Planck Constant
- F) Angular Momentum

2. **Calculate Dimensions of Each Option**:
- **Force (F)**:
- Formula: \( F = m \cdot a \)
- Dimensions: \( [F] = [M][L][T^{-2}] \)

- **Surface Tension (σ)**:
- Formula: \( σ = \frac{F}{L} \)
- Dimensions: \( [σ] = \frac{[F]}{[L]} = \frac{[M][L][T^{-2}]}{[L]} = [M][T^{-2}] \)

- **Angle**:
- An angle is dimensionless (unitless).
- Dimensions: \( [\text{Angle}] = 1 \)

- **Pressure (P)**:
- Formula: \( P = \frac{F}{A} \)
- Dimensions: \( [P] = \frac{[F]}{[L^2]} = \frac{[M][L][T^{-2}]}{[L^2]} = [M][L^{-1}][T^{-2}] \)

- **Planck Constant (h)**:
- Formula: \( h = \frac{E}{f} \)
- Dimensions of Energy (E): \( [E] = [M][L^2][T^{-2}] \)
- Dimensions of Frequency (f): \( [f] = [T^{-1}] \)
- Dimensions: \( [h] = \frac{[E]}{[f]} = \frac{[M][L^2][T^{-2}]}{[T^{-1}]} = [M][L^2][T^{-1}] \)

- **Angular Momentum (L)**:
- Formula: \( L = I \cdot \omega \)
- Dimensions of Moment of Inertia (I): \( [I] = [M][L^2] \)
- Dimensions of Angular Velocity (ω): \( [ω] = [T^{-1}] \)
- Dimensions: \( [L] = [I][ω] = [M][L^2][T^{-1}] \)

3. **Compare Dimensions**:
- Force: \( [M][L][T^{-2}] \)
- Surface Tension: \( [M][T^{-2}] \)
- Angle: \( 1 \) (dimensionless)
- Pressure: \( [M][L^{-1}][T^{-2}] \)
- Planck Constant: \( [M][L^2][T^{-1}] \)
- Angular Momentum: \( [M][L^2][T^{-1}] \)

4. **Identify the Odd One Out**:
- Comparing the dimensions, we can see:
- Force and Surface Tension have different dimensions.
- Angle is dimensionless.
- Pressure has a different dimension from Force and Surface Tension.
- Planck Constant and Angular Momentum have the same dimensions.

5. **Conclusion**:
- The options that do not have the same dimensions are **Force and Surface Tension**.

### Final Answer:
**The correct option is A) Force and Surface Tension do not have the same dimensions.**