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  • Need explanation for: - Motion of System Of Particles and Rigid Body - NEET

The moment of the force , \overset {\rightarrow }F = 4 \hat{i} + 5 \hat{j} - 6 \hat{k} at (2, 0 , -3 ) ,about the point (2, -2 , -2 ) is given by

  • Option 1)

    -7 \hat{i} - 8 \hat{j} - 4 \hat{k}

  • Option 2)

    -4 \hat{i} - \hat{j} - 8 \hat{k}

  • Option 3)

    -8 \hat{i} - 4 \hat{j} - 7 \hat{k}

  • Option 4)

    -7 \hat{i} - 4 \hat{j} - 8 \hat{k}

 

Answers (1)

best_answer

As we have learned

Torque -

underset{ au }{ ightarrow}= underset{r}{ ightarrow} imes underset{F}{ ightarrow}   

 

- wherein

This can be calculated by using either  au=r_{1}F; or; au=rcdot F_{1}

r_{1} = perpendicular distance from origin to the line of force.

F_{1} = component of force perpendicular to line joining force.

 

 

 

 \vec{r}=\vec{r_{2}}-\vec{r_{1}}^

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

=-\hat{k}+2\hat{j}

\therefore \tau =\vec{r}\times \vec{F}

=\left ( 2\hat{j}-\hat{k} \right )\times (4\hat{i}+5\hat{j}-6\hat{k})

=\begin{vmatrix} \hat{i} & \hat{j} & \hat{k}\\ 0& 2& -1\\ 4&5 & -6 \end{vmatrix}=\hat{i}(-12+5)-\hat{j}(0+4)+\hat{k}(0-8)

-7\hat{i}-4\hat{j}-8\hat{k}

 

 

 

 


Option 1)

-7 \hat{i} - 8 \hat{j} - 4 \hat{k}

This is incorrect

Option 2)

-4 \hat{i} - \hat{j} - 8 \hat{k}

This is incorrect

Option 3)

-8 \hat{i} - 4 \hat{j} - 7 \hat{k}

This is incorrect

Option 4)

-7 \hat{i} - 4 \hat{j} - 8 \hat{k}

This is correct

Posted by

Aadil

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