# A uniform force of newton acts on a particle of mass 2 kg. Hence the particle is displaced from position meter to position meter. The work done by the force on the particle is: Option 1) 6J Option 2) 13 J Option 3) 15 J Option 4) 9 J

As we learnt in

Definition of work by constant force -

w = $\underset{F}{\rightarrow}.\underset{S}{\rightarrow}$

- wherein

The scalar product of the force vector ($\underset{F}{\rightarrow}$) and the displacement vector ($\underset{S}{\rightarrow}$)

Given  $\vec{F}=3\hat{i}+\hat{j}$

$\vec{r_{1}}=(2\hat{i}+\hat{k})$

$\vec{r_{2}}=\left ( 4\hat{i}+3\hat{j}-\hat{k} \right )$

$\vec{r}=\vec{r_{2}}-\vec{r_{1}}$

$=\left ( 4\hat{i}+3\hat{j}-\hat{k} \right )-\left ( 2\hat{i}+\hat{k} \right )$

$=2\hat{i}+3\hat{j}-2\hat{k}$

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

$=\left ( 3\hat{i} +\hat{j}\right ).\left ( 2\hat{i}+3\hat{j}-2\hat{k} \right )$

$=6+3=9J$

Option 1)

6J

Incorrect

Option 2)

13 J

Incorrect

Option 3)

15 J

Incorrect

Option 4)

9 J

Correct

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