Q. A force $\overrightarrow{F} = - K(y\widehat{i} + x\widehat{j})$ (where $K$ is a positive constant) acts on a particle moving in the $x - y$ plane. Starting from the origin, the particle is taken along the positive $x$-axis to the point ($a,0$) and then parallel to the $y$-axis to the $(a,a)$. The total work done by the force $\overrightarrow{F}$ on the particle is
A) $- 2Ka^{2}$
B) $2Ka^{2}$
C) $- Ka^{2}$
D) $Ka^{2}$
Explanation
(c) Displacement, $\overrightarrow{r} = \left( a\widehat{i} + a\widehat{j} \right) - \left( a\widehat{i} \right) = a\widehat{j}$
$\overrightarrow{F} = - K\left( y\widehat{i} + x\widehat{j} \right) = - K(a\widehat{i} + a\widehat{j})$
Workdone, $W = \overrightarrow{F}.\overrightarrow{r}$
$= - K\left( a\widehat{i} + a\widehat{j} \right).a\widehat{j} = - Ka^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.