Question

A body is displaced from ${\overrightarrow{r}}_A=(2m,4m,-6m)$ to $\overrightarrow{r_B}=(6\hat{i}-4\hat{j}+2\hat{k})$ m under a constant force $\overrightarrow{F}=(2\hat{i}+3\hat{j}-\hat{k})N.$ Find the work done.

• A. $-24J$
• B. $24J$
• C. $12J$
• D. $-12J$

Answer 1

The correct option is A $-24J$

${\overrightarrow{r}}_A=(2\hat{i}+4\hat{j}-6\hat{k})m$
$\overrightarrow{S}={\overrightarrow{r}}_B-{\overrightarrow{r}}_A$
$=(6\hat{i}-4\hat{j}+2\hat{k})-(2\hat{i}+4\hat{j}-6\hat{k})$
$=4\hat{i}-8\hat{j}+8\hat{k}$
$W=\overrightarrow{F}\cdot \overrightarrow{S}=(2\hat{i}+3\hat{j}-\hat{k})\cdot (4\hat{i}-8\hat{j}+8\hat{k})=8-24-8=-24J$