Question

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

• A. $\frac{3}{2}$
• B. $2$
• C. $1$
• D. $\frac{1}{2}$

Answer 1

Answer: (C)

$W=\int\limits^{\overrightarrow{r_g}}_{\overrightarrow{r_i}}\overrightarrow{F}. d\overrightarrow{r}$
$W=\int\limits^{0}_{1} -xdx +$$\int\limits^{1}_{{0}}ydy$
$W=\frac{-x^{2}}{2}\left|^{^0}_{_{_1}}+\frac{y^{2}}{2}\right|^{^1}_{_{_0}}$
$=\left(\frac{0^{2}}{2}-\frac{1^{2}}{2}\right)+\left(\frac{1^{2}}{2}-\frac{0^{2}}{2}\right)$
$W=1\,J$