Question

A particle moves from position $\overrightarrow{r_1}=3\hat{i}+2\hat{j}-6\hat{k}$ to position $\overrightarrow{r_2}=14\hat{i}+13\hat{j}+9\hat{k}$ under the force $4\hat{i}+\hat{j}+3\hat{k}$. Find the work done.

• A. $10J$
• B. $100J$
• C. $0.01J$
• D. $1J$

Answer 1

The correct option is B $100J$

$\text{Step 1: Displacement vector}$

Displacement vector $={\overrightarrow{r}}_2-{\overrightarrow{r}}_1$

$\Delta \overrightarrow{r}=(14\hat{i}+13\hat{j}+9\hat{k})-(3\hat{i}+2\hat{j}-6\hat{k})$

$\Delta \overrightarrow{r}=11\hat{i}+11\hat{j}+15\hat{k}$

$\text{Step 2: Work done}$

Work done by constant force is given by:

$W=\overrightarrow{F}.\Delta \overrightarrow{r}$

$W=(4\hat{i}+\hat{j}+3\hat{k}).(11\hat{i}+11\hat{j}+15\hat{k})$

$W=100J$

Hence $B$ is the correct option.