A force F = (5î + 3ĵ) N is applied over a particle which displaces it from its origin to the point r= (2î -1ĵ) metres. The work done on the particle is

The correct option is +7 J.

Step-by-step Explanation:

Work done by a constant force on a particle is defined as the dot product (scalar product) of the force vector and the displacement vector.

The formula for work done is given by:
$W=\overrightarrow{F}\cdot \overrightarrow{d}$
where:

$\overrightarrow{F}$ is the force vector, and
$\overrightarrow{d}$ is the displacement vector.

From the question, we are given:
$\overrightarrow{F}=5\hat{i}+3\hat{j}$
The particle is displaced from the origin:
${\overrightarrow{r}}_i=0\hat{i}+0\hat{j}$
to the final point:
${\overrightarrow{r}}_f=2\hat{i}-1\hat{j}$

The displacement vector ($\overrightarrow{d}$) is computed as:
$\overrightarrow{d}={\overrightarrow{r}}_f-{\overrightarrow{r}}_i=2\hat{i}-1\hat{j}$

Now, we substitute these vectors into the work formula to compute the dot product:
$W=(5\hat{i}+3\hat{j})\cdot (2\hat{i}-1\hat{j})$

Multiply the corresponding components together:
$W=(5\cdot 2)+(3\cdot (-1\left)\right)$
$W=10-3$
$W=7\text{J}$

Therefore, the work done on the particle is +7 J.