Allied & ICAR Exam Bank • ALLIED_2684 NAT • 2 Marks

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Physical interpretations – line, surface and volume integrals

Question Statement:

The work done by the conservative force field $\vec{F} = 2x\hat{i} + 3y^2\hat{j}$ in moving a particle from $(0, 0)$ to $(2, 1)$ is:

Answer Key:

5

Step-by-Step Solution & Explanation

Potential function is $\phi = x^2 + y^3$. Work done is $\phi(2, 1) - \phi(0, 0) = (2^2 + 1^3) - 0 = 4 + 1 = 5$.
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