Question

A particle moves from a point $(-2\hat{i}+5\hat{j})\text{m}$ to $(4\hat{j}+3\hat{k})\text{m}$ when a force of $(4\hat{i}+3\hat{j})\text{N}$ is applied. Then, work done by the force is

• A. $8\text{J}$
• B. $11\text{J}$
• C. $5\text{J}$
• D. $2\text{J}$

Answer 1

The correct option is C $5\text{J}$

Initial position vector, ${\overrightarrow{r}}_1=(-2\hat{i}+5\hat{j})\text{m}$
Final position vector, ${\overrightarrow{r}}_2=(4\hat{j}+3\hat{k})\text{m}$
Displacement of the particle is,
$\overrightarrow{r}={\overrightarrow{r}}_2-{\overrightarrow{r}}_1=(2\hat{i}-1\hat{j}+3\hat{k})\text{m}$
$\overrightarrow{F}=(4\hat{i}+3\hat{j})\text{N}$
Since the force is constant, the work done by the force is given by,
$W=\overrightarrow{F}.\overrightarrow{r}$
$\Rightarrow W=(4\hat{i}+3\hat{j}).(2\hat{i}-1\hat{j}+3\hat{k})$
$\Rightarrow W=(4\times 2)+(3\times -1)+(0\times 3)$
$\therefore W=5\text{J}$
Work done by the force is $5\text{J}$