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

Answer 1

The correct option is C $1$

Work done, $W=\int \overrightarrow{F}\cdot \overrightarrow{ds}$

Here, $\overrightarrow{F}\cdot \overrightarrow{ds}=(-x\hat{i}+y\hat{j}).(dx\hat{i}+dy\hat{j})=-xdx+ydy$

$\Rightarrow W=-{\int }_1^{0}xdx+{\int }_0^{1}ydy$

$=(0+\frac{1}{2})+\frac{1}{2}=1\text{J}$

Hence, $\left(C\right)$ is the correct answer,