A body of mass `(1)/(4) kg` moving with velocity `12 m//s` is stopped by applying a force of 0.6 N. Then impulse is :-

Options

A. 7.2 Ns
B. 3 Ns
C. 2.4 Ns
D. None

Answer

To solve the problem, we need to calculate the impulse experienced by the body when a force is applied to stop it. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Mass of the body, \( m = \frac{1}{4} \, \text{kg} \)
- Initial velocity, \( v_i = 12 \, \text{m/s} \)
- Final velocity, \( v_f = 0 \, \text{m/s} \) (since the body is stopped)
- Force applied, \( F = 0.6 \, \text{N} \)

### Step 2: Calculate the change in momentum
The change in momentum (\( \Delta p \)) can be calculated using the formula:
\[ \Delta p = m \cdot (v_f - v_i) \]
Substituting the values:
\[ \Delta p = \frac{1}{4} \cdot (0 - 12) = \frac{1}{4} \cdot (-12) = -3 \, \text{kg m/s} \]
The magnitude of the change in momentum is \( 3 \, \text{kg m/s} \).

### Step 3: Relate impulse to change in momentum
Impulse (\( J \)) is defined as the change in momentum:
\[ J = \Delta p \]
Thus, the impulse is:
\[ J = -3 \, \text{kg m/s} \]
The magnitude of the impulse is \( 3 \, \text{N s} \) (since \( 1 \, \text{kg m/s} = 1 \, \text{N s} \)).

### Step 4: Conclusion
The impulse experienced by the body is \( 3 \, \text{N s} \).

### Final Answer
The impulse is \( 3 \, \text{N s} \).

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