The dimensions of linear impulse are equal to that of

Options

A. Force
B. linear momentum
C. Pressure
D. angular momentum

Explanation

To determine the dimensions of linear impulse and compare them with the dimensions of other physical quantities, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Linear Impulse**:
Linear impulse is defined as the change in linear momentum. Mathematically, it can be expressed as:
\[ \text{Impulse} = \Delta P = P_f - P_i \]
where \( P_f \) is the final momentum and \( P_i \) is the initial momentum.

2. **Define Linear Momentum**:
Linear momentum (P) is given by the product of mass (m) and velocity (v):
\[ P = mv \]

3. **Calculate Change in Linear Momentum**:
If the initial velocity is \( v_1 \) and the final velocity is \( v_2 \), then:
\[ P_i = mv_1 \quad \text{and} \quad P_f = mv_2 \]
Therefore, the change in linear momentum is:
\[ \Delta P = mv_2 - mv_1 = m(v_2 - v_1) \]

4. **Determine the Dimensions of Linear Momentum**:
The dimensions of mass (m) are \([M]\) and the dimensions of velocity (v) are \([L T^{-1}]\). Thus, the dimensions of linear momentum are:
\[ [P] = [m][v] = [M][L T^{-1}] = [M L T^{-1}] \]

5. **Dimensions of Linear Impulse**:
Since linear impulse is equal to the change in linear momentum, its dimensions are the same as that of linear momentum:
\[ [\Delta P] = [M L T^{-1}] \]

6. **Compare with Other Options**:
Now we compare the dimensions of linear impulse with the provided options:
- **Force**: Dimensions of force are \([M L T^{-2}]\).
- **Linear Momentum**: Dimensions are \([M L T^{-1}]\).
- **Pressure**: Dimensions are \([M L^{-1} T^{-2}]\).
- **Angular Momentum**: Dimensions are \([M L^2 T^{-1}]\).

From this comparison, we see that the dimensions of linear impulse match the dimensions of linear momentum.

### Conclusion:
Thus, the dimensions of linear impulse are equal to that of linear momentum.

### Final Answer:
**The dimensions of linear impulse are equal to that of linear momentum.**

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