Question

A particle moves from a point $(-2\hat{i}+5\hat{j})$ to $(4\hat{j}+3\hat{k})$ when a force of $(4\hat{i}+3\hat{j})N$ is applied. How much work has been done by the force?

• A. $5J$
• B. $2J$
• C. $8J$
• D. $11J$

Answer 1

The correct option is A $5J$

Given $\overrightarrow{F}=4\hat{i}+3\hat{j}$, Position ${\overrightarrow{r}}_1=-2\hat{i}+5\hat{j}$ and ${\overrightarrow{r}}_2=4\hat{j}+3\hat{k}$

$\therefore$ Displacement, $\overrightarrow{d}={\overrightarrow{r}}_2-{\overrightarrow{r}}_1=2\hat{i}-\hat{j}+3\hat{k}$

$\therefore$ Work done $=\overrightarrow{F}.\overrightarrow{d}=(4\hat{i}+3\hat{j}).(2\hat{i}-\hat{j}+3\hat{k})=8-3=5J$