Question

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

• A. $+10$
• B. $+7$
• C. $-7$
• D. $+13$

Answer 1

The correct option is B $+7$

Given constant force $\overrightarrow{F}=(5\hat{i}+3\hat{j}+2\hat{k})\text{N}$
Initial position $\overrightarrow{r_1}=(0\hat{i}+0\hat{j}+0\hat{k})\text{m}$, as starting from origin.
Final position $\overrightarrow{r_2}=(2\hat{i}-\hat{j}+0\hat{k})\text{m}$

To find the displacement $\overrightarrow{s}$:
$\overrightarrow{s}=\overrightarrow{r_2}-\overrightarrow{r_1}=$ change in position
$\overrightarrow{s}=(2\hat{i}-\hat{j}+0\hat{k})-(0\hat{i}+0\hat{j}+0\hat{k})$
$\overrightarrow{s}=(2\hat{i}-\hat{j})\text{m}$

Hence the work done , $W=\overrightarrow{F}.\overrightarrow{S}$
$W=(5\hat{i}+3\hat{j}+2\hat{k}).(2\hat{i}-\hat{j})=10-3=7\text{J}$

Hence option B is the correct answer.