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Physics · WORK, ENERGY AND POWER
हिन्दीA particle moves along the x-axis under a conservative force having potential energy \( V(x) = 2x^3 - 9x^2 + 12x \text{ J} \), where \( x \) is in meters. The work done by this conservative force as the particle moves from \( x = 1\text{ m} \) to \( x = 3\text{ m} \) is:
Correct answer · Option 1
\( -4\text{ J} \)
Explanation
Work done by a conservative force is \( W = V(x_1) - V(x_2) \). Here \( V(1) = 2(1)^3 - 9(1)^2 + 12(1) = 5\text{ J} \) and \( V(3) = 2(27) - 9(9) + 12(3) = 54 - 81 + 36 = 9\text{ J} \). Thus, \( W = V(1) - V(3) = 5 - 9 = -4\text{ J} \).
