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