For a given change in linear momentum when time of impact increases force .

Options

A. decreases
B. increases
C. remains same
D. none of the above

Answer

To solve the problem, we need to analyze the relationship between force, time, and change in linear momentum. Here’s a step-by-step solution:

### Step 1: Understand the relationship between force, time, and momentum
The impulse experienced by an object is equal to the change in its momentum. Mathematically, this can be expressed as:
\[ \text{Impulse} = \text{Force} \times \text{Time} = \Delta p \]
where \( \Delta p \) is the change in momentum.

### Step 2: Rearranging the equation
From the impulse-momentum theorem, we can rearrange the equation to express force:
\[ \text{Force} = \frac{\Delta p}{\text{Time}} \]

### Step 3: Analyze the effect of time on force
In this scenario, we are given that the change in linear momentum \( \Delta p \) is constant. This means that the numerator in our force equation remains unchanged.

### Step 4: Consider the impact of increasing time
If the time of impact increases while keeping \( \Delta p \) constant, we can substitute this into our force equation:
\[ \text{Force} = \frac{\Delta p}{\text{Time}} \]
As the time increases, the denominator increases. Since the numerator is constant, an increase in the denominator will result in a decrease in the overall value of force.

### Step 5: Conclusion
Therefore, when the time of impact increases, the force must decrease in order to keep the change in momentum constant.

### Final Answer
The force decreases.