Question

A particle is shifted from point $(0,0,1\text{m})$ to $(1\text{m},1\text{m},2\text{m})$, under the simultaneous action of several forces. Two of the forces are $\overrightarrow{F_1}=(2\hat{i}+3\hat{j}-\hat{k})\text{N}$ and $\overrightarrow{F_2}=(\hat{i}-2\hat{j}+2\hat{k})\text{N}$. Find the work done by these two forces

• A. $7\text{J}$
• B. $5\text{J}$
• C. $10\text{J}$
• D. $12\text{J}$

Answer 1

The correct option is B $5\text{J}$

As particle is shifted from point $(0,0,1\text{m})$ to $(1\text{m},1\text{m},2\text{m})$
Displacement vector $\Delta \overrightarrow{r}=(\hat{i}+\hat{j}+\hat{k})$
net force acting is $\overrightarrow{F_1}+\overrightarrow{F_2}=(2\hat{i}+3\hat{j}-\hat{k})\text{N}+(\hat{i}-2\hat{j}+2\hat{k})\text{N}=(3\hat{i}+\hat{j}+\hat{k})$
Work done by a constant force equals to the dot product of the force and displacement vectors.
$W=\overrightarrow{F}.\Delta \overrightarrow{r}\Rightarrow W=(\overrightarrow{F_1}+\overrightarrow{F_2}).\Delta \overrightarrow{r}$
Substituting the given values, we have $W=(3\hat{i}+\hat{j}+\hat{k}).(\hat{i}+\hat{j}+\hat{k})=3+1+1=5\text{J}$