A uniform force of \left ( 3\ \hat{i}+\hat{j} \right ) newton acts on a particle of mass 2 kg. Hence the particle is displaced from position

\left ( 2\ \hat{i}+\hat{k} \right ) meter to position \left ( 4\ \hat{i}+3\hat{j}-\hat{k} \right ) 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

 

Answers (1)

As we learnt in

Definition of work by constant force -

w = underset{F}{
ightarrow}.underset{S}{
ightarrow}

- wherein

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

 

 

 

 

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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