Work Energy Power

JEE Main level, single correct, medium

43 of 183

Question 43 of 183

Potential energy (VV) versus distance (xx) is given by the graph. Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low.

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Answer: (D) FBC>FAB>FDE>FCDF_{B C}\gt F_{A B}\gt F_{D E}\gt F_{C D}

Force is related to potential energy by F=−dVdxF = -\frac{dV}{dx}.
Magnitude of force ∣F∣=∣dVdx∣|F| = \left|\frac{dV}{dx}\right| = |slope of V-x graph|
From graph coordinates: A(1, 0), B(1.5, 1), C(2, 4), D(4, 4), E(5, 3)
∣FAB∣=1−01.5−1=2|F_{AB}| = \frac{1-0}{1.5-1} = 2
∣FBC∣=4−12−1.5=6|F_{BC}| = \frac{4-1}{2-1.5} = 6
∣FCD∣=4−44−2=0|F_{CD}| = \frac{4-4}{4-2} = 0
∣FDE∣=∣3−4∣5−4=1|F_{DE}| = \frac{|3-4|}{5-4} = 1
Ranking: FBC>FAB>FDE>FCDF_{BC} \gt F_{AB} \gt F_{DE} \gt F_{CD}

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