Question

An object is displaced from point A(2m, 3m, 4m) to a point B (1m, 2m, 3m) under a constant force $\overrightarrow{F}=(2\hat{i}+3\hat{j}+4\hat{k})N.$ Find the work done by this force in this process.

• A. $-9J$
• B. $9J$
• C. $-18J$
• D. $18J$

Answer 1

The correct option is A $-9J$

Since, $\overrightarrow{F}$ = constant, we can use.
$W=\overrightarrow{F}\bullet \overrightarrow{S}$

Here, $\overrightarrow{S}={\overrightarrow{r}}_f-{\overrightarrow{r}}_i=(\hat{i}+2\hat{j}+3\hat{k})-(2\hat{i}+3\hat{j}+4\hat{k})$

$=(-\hat{i}-\hat{j}-\hat{k})$

$\therefore W=(2\hat{i}+3\hat{j}+4\hat{k})\bullet (-\hat{i}-\hat{j}-\hat{k})$

$=-2-3-4=-9J$