Question

A particle is displaced from a position $(2\hat{i}-\hat{j}+\hat{k})$ to another position $(3\hat{i}+2\hat{j}-2\hat{k})$ under the action of the force $(2\hat{i}+\hat{j}-\hat{k}).$ The work done by the force in arbitrary unit is

• A. 8
• B. 10
• C. 12
• D. 16

Answer 1

Answer: (A)

Here, ${\vec{r}}_1=2\hat{i}-\hat{j}+\hat{k},{\vec{r}}_2=3\hat{i}+2\hat{j}-2\hat{k}$
$\vec{F}=2\hat{i}+\hat{j}-\hat{k}$
Displacement, $\vec{r}={\vec{r}}_2-{\vec{r}}_1$
$=(3\hat{i}+2\hat{j}-2\hat{k})-(2\hat{i}-\hat{j}+\hat{k})$
$=\hat{i}+3\hat{j}-3\hat{k}$
$W=\vec{F}\cdot \vec{r}=(2\hat{i}+\hat{j}-\hat{k})\cdot (\hat{i}+3\hat{j}-3\hat{k})$
$=2+3+3=8\text{ units }$