The unit of impulse is the same as that of

Options

A. Force
B. Acceleration
C. Momentum
D. Energy

Answer

To solve the question regarding the unit of impulse and its equivalence to other physical quantities, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Impulse**:
Impulse is defined as the change in momentum of an object when a force is applied over a period of time. Mathematically, impulse (J) can be expressed as:
\[ J = \Delta p = p_{final} - p_{initial} \]
where \( p \) is momentum.

2. **Determine the Unit of Impulse**:
Since impulse is the change in momentum, we need to find the unit of momentum. Momentum (p) is defined as:
\[ p = mv \]
where \( m \) is mass and \( v \) is velocity. The unit of mass (m) is kilograms (kg), and the unit of velocity (v) is meters per second (m/s). Therefore, the unit of momentum is:
\[ [p] = [m][v] = \text{kg} \cdot \text{m/s} = \text{kg m/s} \]

3. **Identify the Dimensions of Impulse**:
The dimension of impulse can also be expressed in terms of mass (M), length (L), and time (T). Since momentum has the dimension:
\[ [p] = MLT^{-1} \]
Thus, the dimension of impulse is also:
\[ [J] = MLT^{-1} \]

4. **Compare with Other Quantities**:
Now, we will compare the dimensions of impulse with the dimensions of the other options provided:
- **Force (F)**: The unit of force is given by Newton (N), which can be expressed as:
\[ [F] = MLT^{-2} \]
- **Acceleration (a)**: The unit of acceleration is:
\[ [a] = LT^{-2} \]
- **Momentum (p)**: As calculated earlier:
\[ [p] = MLT^{-1} \]
- **Energy (E)**: The unit of energy (work done) is:
\[ [E] = ML^2T^{-2} \]

5. **Conclusion**:
From the above comparisons, we can see that the dimension of impulse (MLT^{-1}) is the same as that of momentum (MLT^{-1}). Therefore, the correct answer to the question is:
\[ \text{The unit of impulse is the same as that of momentum.} \]

### Final Answer:
The unit of impulse is the same as that of **momentum**.

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