Question

Consider a force $\overset{ \rightarrow }{F}=-x\hat{i}+y\hat{j}$ . The particle is moved from point $A\left(\right.1,0\left.\right)$ to $B\left(\right.0,1\left.\right)$ along the line segment. The work done by force is
(All quantities are in SI units)

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

Answer 1

Answer: (D)

$W=\displaystyle \int \overset{ \rightarrow }{F}\cdot d\overset{ \rightarrow }{s}$
$=\left(\right.-x\hat{i}+yj\left.\right)\cdot \left(\right.dx\hat{i}+dy\hat{j}\left.\right)$
$=\displaystyle \int _{1}^{0}-xdx+\displaystyle \int _{0}^{1}ydy$
$=-\frac{x^{2}}{2}\right|_{1}^{0}+\frac{y^{2}}{2}\right|_{1}^{0}==\left(0 + \frac{1}{2}\right)+\left(\frac{1}{2}\right)=1J$