Physics - W.E.P. Question with Solution | TestHub

As force is a function of $r$, therefore
$W={\int }_{\left(\mathrm{0,0}\right)}^{\left(\mathrm{1,1}\right)}\overrightarrow{F}.\overrightarrow{d}x$
Here $d\overrightarrow{s}=dx\hat{\mathrm{i}}+dy\hat{\mathrm{j}}+dz\hat{\mathrm{k}}$

$\therefore$ $W={\int }_{\left(\mathrm{0,0}\right)}^{\left(\mathrm{1,1}\right)}\left(x^{2}dy+ydx\right)={\int }_{\left(\mathrm{0,0}\right)}^{\left(\mathrm{1,1}\right)}\left(y^{2}dy+xdx\right)$     (as $x=y$ )
$\therefore$ $W={\left[\frac{y^3}{3}+\frac{x^2}{2}\right]}_{\left(\mathrm{0,0}\right)}^{\left(\mathrm{1,1}\right)}=\frac{5}{6} \mathrm{J}$