Question

A particle moves from a point $\left(-2\hat{i}+5\hat{j}\right)$ to $\left(4\hat{j}+3\hat{k}\right)$ when a force of $\left(4\hat{i}+3\hat{j}\right)$$N$ is applied. How much work has been done by the force ?

• A. $5J$
• B. $2J$
• C. $8J$
• D. $11J$

Answer 1

The correct option is A $5J$

Displacement of the particle
$\overrightarrow{S}=(4\hat{j}+3\hat{k})-(-2\hat{i}+5\hat{j})$
$=2\hat{i}-\hat{j}+3\hat{k}$
Force acting on the particle
$\overrightarrow{F}=4\hat{i}+3\hat{j}$
$\therefore$ Work done
$W=\overrightarrow{F}.\overrightarrow{S}$
$=(4\hat{i}+3\hat{j}).(2\hat{i}-\hat{j}+3\hat{k})$
$=8+(-3)=5J$