Question

A force $\overrightarrow{F}=(5\hat{i}+3\hat{j}+2\hat{k})\text{N}$ is applied over a particle which displaces it from origin to the point $\overrightarrow{r}=(2\hat{i}-\hat{j})\text{m}$. The work done on the particle is

• A. $+5\text{J}$
• B. $+7\text{J}$
• C. $+10\text{J}$
• D. $+13\text{J}$

Answer 1

The correct option is B $+7\text{J}$

Particle's initial position, ${\overrightarrow{r}}_i=(0\hat{i}+0\hat{j})\text{m}$
Particle's final position, ${\overrightarrow{r}}_f=(2\hat{i}-\hat{j})\text{m}$
Hence displacement of particle is given by,
$\overrightarrow{S}={\overrightarrow{r}}_f-{\overrightarrow{r}}_i$
$\Rightarrow \overrightarrow{S}=(2\hat{i}-\hat{j})-(0\hat{i}+0\hat{j})=(2\hat{i}-\hat{j})\text{m}$
Hence workdone by force is:
$W=\overrightarrow{F}.\overrightarrow{S}$
$W=(5\hat{i}+3\hat{j}+2\hat{k}).(2\hat{i}-\hat{j})$
$W=(5\times 2)+(3\times (-1\left)\right)+(2\times 0)$
$\therefore W=10-3=7\text{J}$