The dimensions of impulse are equal to that of

Options

A. Pressure
B. Linear momentum
C. Force
D. Angular momentum

Answer

To find the dimensions of impulse and determine which physical quantity it is equal to, we can follow these steps:

### Step 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:
\[ J = F \cdot \Delta t \]
where \( F \) is the net force applied and \( \Delta t \) is the time duration for which the force is applied.

### Step 2: Determine the Dimensions of Force
The force \( F \) can be expressed using Newton's second law:
\[ F = m \cdot a \]
where \( m \) is mass and \( a \) is acceleration. The dimensions of mass (m) are \([M]\) and the dimensions of acceleration (a) are \([L][T^{-2}]\). Therefore, the dimensions of force are:
\[ [F] = [M][L][T^{-2}] = [M L T^{-2}] \]

### Step 3: Determine the Dimensions of Time
The dimensions of time (\( \Delta t \)) are simply:
\[ [T] \]

### Step 4: Combine the Dimensions to Find Impulse
Now, substituting the dimensions of force and time into the impulse equation:
\[ [J] = [F] \cdot [T] = [M L T^{-2}] \cdot [T] = [M L T^{-1}] \]

### Step 5: Identify the Physical Quantity with the Same Dimensions
Now that we have established that the dimensions of impulse are \([M L T^{-1}]\), we can compare this with other physical quantities:

1. **Pressure**: Dimensions are \([M L^{-1} T^{-2}]\) - Not equal.
2. **Linear Momentum**: Dimensions are \([M L T^{-1}]\) - Equal.
3. **Force**: Dimensions are \([M L T^{-2}]\) - Not equal.
4. **Angular Momentum**: Dimensions are \([M L^{2} T^{-1}]\) - Not equal.

### Conclusion
The dimensions of impulse are equal to that of linear momentum.

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

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