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Consider a force $\overrightarrow{\mathrm{F}}=-x \hat{i}+y \hat{j}$. 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)

  1. 2

  2. $\frac{1}{2}$

  3. 1

  4. $\frac{3}{2}$

Correct Option: , 3


(3) Work done, $W=\int \vec{F} \cdot \overrightarrow{d s}$

$=(-x \hat{i}+y \hat{j}) \cdot(d \times \hat{i}+d y \hat{j})$

$\Rightarrow W=-\int_{1}^{0} x d x+\int_{0}^{1} y d y$

$=\left(0+\frac{1}{2}\right)+\frac{1}{2}=1 J$

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