Question

A force $\overrightarrow{F}=(5\hat{i}+3\hat{j})$ N is applied on a particle which displaces it to the point $\overrightarrow{r}=(2\hat{i}-\hat{j})$ m from the origin. The work done on the particle is

• A. -7 J
• B. +13 J
• C. +7 J
• D. 11 J

Answer 1

The correct option is C +7 J

Given
$\overrightarrow{F}=5\hat{i}+3\hat{j}$
$\overrightarrow{r}=2\hat{i}-\hat{j}$
The work done on the particle is a scalar product of F and r, hence
$W=F.r$
$W=(5\hat{i}+3\hat{j}).(2\hat{i}-\hat{j})$
$W=10-3=+7J$