Figures (a), (b), (c) and (d) show variation of force with time.… - Solution | JEE Physics

MCQEasyJEE 2023Impulse & Momentum

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

Answer

Correct answer:B

Standard Method

Given: Four force-time graphs are shown.

Find: Which figure has the highest impulse.

Impulse is equal to the area under the force-time graph.

For Fig (a):

\text{Impulse} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 1 \times 0.5 = 0.25 \, \text{Ns}

For Fig (b):

\text{Impulse} = \text{length} \times \text{width} = 2 \times 0.5 = 1 \, \text{Ns}

For Fig (c):

\text{Impulse} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 1 \times 0.75 = 0.375 \, \text{Ns}

For Fig (d):

\text{Impulse} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \times 0.5 = 0.5 \, \text{Ns}

Comparing all values, the highest impulse is $1 \, \text{Ns}$ for Fig (b).

Therefore, the correct option is B.

Treating impulse as the maximum force instead of the area under the force-time graph is incorrect. A taller graph does not always mean a larger impulse. Always compare the total enclosed area.
Using the triangle area formula for every graph is wrong because Fig (b) is a rectangle. Identify the shape first, then apply the correct area formula.
Ignoring the time duration leads to an incorrect comparison. Impulse depends on both force and time, so a smaller force acting for longer time can produce a larger impulse.

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