Question

Work done by a force $F=(\hat{i}+2\hat{j}+3\hat{k})\text{N}$ acting on a particle in displacing it from the point $\overrightarrow{r_1}=\hat{i}+\hat{j}+\hat{k}$ to the point $\overrightarrow{r_2}=\hat{i}-\hat{j}+2\hat{k}$ is

• A. $-3\text{J}$
• B. $-1\text{J}$
• C. zero
• D. $2\text{J}$

Answer 1

The correct option is B $-1\text{J}$

As we know that work done is given by

$W=\overrightarrow{F}\cdot \overrightarrow{S}=\overrightarrow{F}\cdot ({\overrightarrow{r}}_2-{\overrightarrow{r}}_1)$

$W=(\hat{i}+2\hat{j}+3\hat{k})\cdot \left[\right(\hat{i}-\hat{j}+2\hat{k})-(\hat{i}+\hat{j}+\hat{k}\left)\right]$

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

$W=-4+3=-1\text{J}$

So, option $\left(b\right)$ is correct.

Why this question ? In case of constant force, the work done is, $W=\overrightarrow{F}.\overrightarrow{S}$ $W=(F_x\hat{i}+F_y\hat{j}+F_z\hat{k})\cdot (S_x\hat{i}+S_y\hat{j}+S_z\hat{k})$ $W=F_x{S}_x+F_y{S}_y+F_z{S}_z$