Question

A particle is displaced from a position $(2\hat{i}-\hat{j}+\hat{k})$ metre to another position $(3\hat{i}+2\hat{j}-2\hat{k})$ metre under the action of force $(2\hat{i}+\hat{j}-\hat{k})N$. Work done by the force is

• A. $8J$
• B. $10J$
• C. $12J$
• D. $36J$

Answer 1

The correct option is A $8J$

$\text{Step 1: Finding Displacement vector for calculating Work done}$

$\overrightarrow{\Delta r}=\overrightarrow{r_2}-\overrightarrow{r_1}$

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

$\therefore \overrightarrow{\Delta r}=(\hat{i}+3\hat{j}-3\hat{k})$

$\text{Step 2: Calculation of workdone}$

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

$\Rightarrow W=(2i+j-k)$. $(i+3j-3k)$

$\Rightarrow W=2+3+3=8J$

$\therefore$ Work Done by the force is $8J$

Hence, Option A is correct.