Question

A particle moves from a point (-1 m, 2 m) to (1 m, 2 m)due to a force acting on it. If the force is $\overrightarrow{F}=4\stackrel{\wedge }{i}N$, then work done by this force is :

• A. Zero
• B. 4 J
• C. 8 J
• D. 10 J

Answer 1

Answer: (C)

8 J

The vector at point $A(-1,2)$ is

${\overrightarrow{r}}_1=-\hat{i}+2\hat{j}$

The vector at point $B(1,2)$ is

$r_2=\hat{i}+2\hat{j}$

Displacement vector, $\overrightarrow{r}={\overrightarrow{r}}_2-{\overrightarrow{r}}_1$

$\overrightarrow{r}=(\hat{i}+2\hat{j})-(-\hat{i}+2\hat{j})$

$\overrightarrow{r}=2\hat{i}$

Force, $\overrightarrow{F}=4\hat{i}N$

The work done by the force,

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

$W=\left(4\hat{i}\right).\left(2\hat{i}\right)=8cos{0}^0$

$W=8J$

The correct option is C.