Question

Two forces $\hat{\text{i}}\text{+}\hat{\text{j}}\text{+}\hat{\text{k}}\text{N}\text{and}\hat{\text{i}}\text{+ 2}\hat{\text{j}}\text{+ 3}\hat{\text{k}}\text{N}$ act on a particle and displace it from (2,3,4) to point (5,4,3). Displacement is in m. Work done is:

• A. $5J$
• B. $4J$
• C. $3J$
• D. None of these

Answer 1

The correct option is A $5J$

Given,

${\overrightarrow{F}}_1=\hat{i}+\hat{j}+\hat{k},{\overrightarrow{F}}_2=\hat{i}+2\hat{j}+3\hat{k}$

$F_n=F_1+F_2=2\hat{i}+3\hat{j}+4\hat{k}$

Position vector between two points $(2,3,4)to(5,4,3)$ is

$\overrightarrow{r}=(5-2)\hat{i}+(4-3)\hat{j}+(3-4)\hat{k}$

$\overrightarrow{r}=3\hat{i}+\hat{j}-\hat{k}$

Work done, $W={\overrightarrow{F}}_n.\overrightarrow{r}$

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

$W=2\times 3+3\times 1-4\times 1$

$W=6+3-4=9-4=5J$

The correct option is A.