Momentum has the same units as that of

Options

A. impulse
B. torque
C. moment of momentum
D. couple

Answer

To solve the question "Momentum has the same units as that of", we will analyze the options provided and determine which physical quantity shares the same unit as momentum.

### Step-by-Step Solution:

1. **Understanding Momentum**:
- Momentum (P) is defined as the product of mass (m) and velocity (v).
- The formula for momentum is:
\[ P = m \cdot v \]

2. **Identifying Units of Momentum**:
- The unit of mass (m) is kilograms (kg).
- The unit of velocity (v) is meters per second (m/s).
- Therefore, the unit of momentum is:
\[ \text{Unit of Momentum} = \text{kg} \cdot \text{m/s} = \text{kg m/s} \]

3. **Analyzing the Options**:
- **Option 1: Impulse**:
- Impulse (J) is defined as the change in momentum. Its formula is:
\[ J = F \cdot \Delta t \]
- The unit of force (F) is Newton (N), and the unit of time (Δt) is seconds (s).
- The unit of impulse can also be expressed as:
\[ \text{Unit of Impulse} = \text{N} \cdot \text{s} = \text{(kg m/s}^2) \cdot \text{s} = \text{kg m/s} \]
- Therefore, the unit of impulse is the same as that of momentum.

- **Option 2: Torque**:
- Torque (τ) is defined as the product of force and the distance from the pivot point:
\[ \tau = F \cdot r \]
- The unit of torque is:
\[ \text{Unit of Torque} = \text{N} \cdot \text{m} = \text{(kg m/s}^2) \cdot \text{m} = \text{kg m}^2/\text{s}^2 \]
- This is different from the unit of momentum.

- **Option 3: Moment of Momentum (Angular Momentum)**:
- Moment of momentum (L) is defined as:
\[ L = m \cdot v \cdot r \]
- The unit of angular momentum is:
\[ \text{Unit of Angular Momentum} = \text{kg} \cdot \text{m/s} \cdot \text{m} = \text{kg m}^2/\text{s} \]
- This is also different from the unit of momentum.

4. **Conclusion**:
- From the analysis, we can conclude that the only quantity that shares the same unit as momentum (kg m/s) is impulse.
- Therefore, the answer to the question is:
\[ \text{Momentum has the same units as that of Impulse.} \]