Figures (a), (b), (c) and (d) show variation of force with time The impulse is highest in figure
Figures (a), (b), (c) and (d) show variation of force with time The impulse is highest in figure
Show Hint
Impulse is the area under the force-time graph. Calculate the area for each figure to determine which one has the highest impulse.
- Fig (b)
- Fig (c)
- Fig (a)
- Fig (d)
The Correct Option is A
Solution and Explanation
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).
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Concepts Used:
Newtons Laws of Motion
Newton’s First Law of Motion:
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion:
Newton’s 2nd law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the object’s mass.
Mathematically, we express the second law of motion as follows:
Newton’s Third Law of Motion:
Newton’s 3rd law states that there is an equal and opposite reaction for every action.