The pair of physical quantities having the same dimensional formula are

Options

A. Mometum, impulse
B. Momentum , energy
C. Energy, pressure
D. Force, power

Answer

To determine the pair of physical quantities having the same dimensional formula, we will analyze the dimensional formulas of the given quantities: momentum, impulse, energy, pressure, force, and power.

### Step-by-Step Solution:

1. **Identify the Physical Quantities**: We need to find the dimensional formulas for momentum, impulse, energy, pressure, force, and power.

2. **Calculate the Dimensional Formula of Momentum**:
- Momentum (p) is defined as the product of mass (m) and velocity (v).
- The formula for momentum is:
\[ p = m \cdot v \]
- The dimensional formula for mass (m) is [M].
- The dimensional formula for velocity (v) is [L][T]^{-1} (length per time).
- Therefore, the dimensional formula for momentum is:
\[ [M][L][T]^{-1} = [M L T^{-1}] \]

3. **Calculate the Dimensional Formula of Impulse**:
- Impulse (I) is defined as the product of force (F) and time (t).
- The formula for impulse is:
\[ I = F \cdot t \]
- The dimensional formula for force (F) is [M][L][T]^{-2} (mass times acceleration).
- The dimensional formula for time (t) is [T].
- Therefore, the dimensional formula for impulse is:
\[ [M L T^{-2}][T] = [M L T^{-1}] \]

4. **Compare the Dimensional Formulas**:
- From the calculations, we have:
- Momentum: [M L T^{-1}]
- Impulse: [M L T^{-1}]
- Since both momentum and impulse have the same dimensional formula, they are the correct pair.

5. **Check Other Options**:
- **Energy**: Kinetic energy (KE) is given by:
\[ KE = \frac{1}{2} m v^2 \]
- Dimensional formula: [M][L^2][T^{-2}] = [M L^2 T^{-2}]
- **Pressure**: Pressure (P) is defined as force per unit area:
\[ P = \frac{F}{A} \]
- Dimensional formula: [M L T^{-2}]/[L^2] = [M L^{-1} T^{-2}]
- **Force**: Force (F) as mentioned is:
\[ F = m a \]
- Dimensional formula: [M][L][T^{-2}] = [M L T^{-2}]
- **Power**: Power (P) is defined as work done per unit time:
\[ P = \frac{W}{t} \]
- Dimensional formula: [M L^2 T^{-2}]/[T] = [M L^2 T^{-3}]

6. **Conclusion**:
- The only pair of physical quantities with the same dimensional formula is **momentum and impulse**.

### Final Answer:
The pair of physical quantities having the same dimensional formula are **momentum and impulse**.