Question

A uniform force of $(3\hat{i}+\hat{j})N$ newton acts on a particle of mass $2kg$. Hence the particle is displaced from position $(2\hat{i}+\hat{k})$ meter to position $(4\hat{i}+3\hat{j}-\hat{k})$ meter. The work done by the force on the particle is:-

• A. $15J$
• B. $9J$
• C. $6J$
• D. $13J$

Answer 1

The correct option is B $9J$

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

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

$\therefore$ Work done $=\overrightarrow{F}.\overrightarrow{d}=(3\hat{i}+\hat{j}).(2\hat{i}+3\hat{j}-2\hat{k})=6+3=9J$