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  4. Consider a force F=-x hati+y hatj. The workdone by this force in moving a particle from point P(1,0) to Q(0,1) along the line segment is (all quantities are in SI units).

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Q. Consider a force $F=-x \hat{i}+y \hat{j}$. The workdone by this force in moving a particle from point $P(1,0)$ to $Q(0,1)$ along the line segment is (all quantities are in SI units).Physics Question Image

Work, Energy and Power

Solution:

Work done, $W=\int \vec{F} \cdot \overrightarrow{d s}=(-x \hat{i} \times y \hat{j}) \cdot(x \hat{i}+y \hat{j})$
$\Rightarrow W=\int\limits_1^0 x d x+\int\limits_0^1 y d y=\left(0+\frac{1}{2}\right)+\frac{1}{2}=1 J$