Question

A force $\mathrm{F}=3\mathrm{i}+4\mathrm{j}$ Newton acts on a particle that moves from a position $\left(2\mathrm{m},3\mathrm{m}\right)$ to $\left(3\mathrm{m},0\mathrm{m}\right)$. Then the work done is:

• A. $-9\mathrm{j}$
• B. $9\mathrm{j}$
• C. $5\mathrm{j}$
• D. $-5\mathrm{j}$

Answer 1

The correct option is A

$-9\mathrm{j}$

Step 1: Given data

Force,

$\mathrm{F}=3\mathrm{i}+4\mathrm{j}$

A particle moves from $\left(2\mathrm{m},3\mathrm{m}\right)$ to $\left(3\mathrm{m},0\mathrm{m}\right)$

Step 2: Formula used

The work done by the force is given by

$\mathrm{W}=\overrightarrow{F}.\mathrm{A}\overrightarrow{\mathrm{r}}$

Where,

$\mathrm{F}$ is the force acting on the object, $\mathrm{r}$ is the displacement,

Displacement of the particle is,

$\overrightarrow{∆\mathrm{r}}=\overrightarrow{{\mathrm{r}}_{\mathrm{f}}}-\overrightarrow{{\mathrm{r}}_{\mathrm{i}}}$

Step 2: Calculating the value of work done

Given that,

$$\begin{gathered} \overrightarrow{{\mathrm{r}}_{\mathrm{f}}}=\left(\overrightarrow{3\mathrm{i}}+\overrightarrow{0\mathrm{j}}\right) \\ \overrightarrow{{\mathrm{r}}_{\mathrm{i}}}=\left(\overrightarrow{2\mathrm{i}}+\overrightarrow{3\mathrm{j}}\right) \end{gathered}$$

Displacement, $\overrightarrow{∆\mathrm{r}}=\left(\overrightarrow{\mathrm{i}}-\overrightarrow{3\mathrm{j}}\right)\mathrm{m}$

Thus, Work done is given by $$\begin{gathered} \mathrm{W}=(\overrightarrow{3\mathrm{i}}+\overrightarrow{4\mathrm{j}}).(\overrightarrow{\mathrm{i}}+\overrightarrow{3\mathrm{j}}) \\ =\overrightarrow{-9\mathrm{j}} \end{gathered}$$

Therefore the work done by the force is given by $\overrightarrow{-9\mathrm{j}}$.