Question

Figures (a), (b), (c) and (d) show variation of force with time The impulse is highest in figure

• A. Fig (b)
• B. Fig (c)
• C. Fig (a)
• D. Fig (d)

Hint:

Impulse is the area under the force-time graph. Calculate the area for each figure to determine which one has the highest impulse.

Answer 1

The Correct Option is A

Step 1: Recall the Definition of Impulse

Impulse is defined as the change in momentum, which is equal to the area under the force-time graph.

Step 2: Calculate the Impulse for Each Figure

• (a): Impulse = Area of triangle = \( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 1 \times 0.5 = 0.25 \, \text{Ns} \)
• (b): Impulse = Area of rectangle = \( \text{length} \times \text{width} = 2 \times 0.5 = 1 \, \text{Ns} \)
• (c): Impulse = Area of triangle = \( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 1 \times 0.75 = 0.375 \, \text{Ns} \)
• (d): Impulse = Area of triangle = \( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \times 0.5 = 0.5 \, \text{Ns} \)

Conclusion: Figure (b) has the highest impulse (1 Ns). Therefore, the correct answer is (Option 1).