Question:
Consider a force \(\vec{F}=-x\hat{i}+y\hat{j}\). The work done by this force in moving a particle from point A(1, 0) to B(0, 1) along the line segment is : (all quantities are in SI units)
Consider a force \(\vec{F}=-x\hat{i}+y\hat{j}\). The work done by this force in moving a particle from point A(1, 0) to B(0, 1) along the line segment is : (all quantities are in SI units)
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Integrate \(\vec F\cdot d\vec r=-x\,dx+y\,dy\) from A(1, 0) to B(0, 1).
Updated On: Nov 5, 2026
- 2
- \(\frac{1}{2}\)
- 1
- \(\frac{3}{2}\)
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The Correct Option is C
Solution and Explanation
\(W=\int\vec F\cdot d\vec r=\int(-x\,dx+y\,dy)\).
The x-part: \(-\int_{1}^{0}x\,dx=-\left[\frac{x^2}{2}\right]_1^0=\frac{1}{2}\).
The y-part: \(\int_0^1y\,dy=\frac{1}{2}\).
\(W=\frac{1}{2}+\frac{1}{2}=1\) J.
Answer: (3) 1
The x-part: \(-\int_{1}^{0}x\,dx=-\left[\frac{x^2}{2}\right]_1^0=\frac{1}{2}\).
The y-part: \(\int_0^1y\,dy=\frac{1}{2}\).
\(W=\frac{1}{2}+\frac{1}{2}=1\) J.
Answer: (3) 1
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