If force F → = 3 i ^ + 4 j ^ − 2 k ^ acts on a particle having position vector 2 i ^ + j ^ + 2 k ^ then, the torque about the origin will be:

r → = 2 i ^ + j ^ + 2 k ^ τ → = r → * F → = ( 2 i ^ + j ^ + 2 k ^ ) * ( 3 i ^ + 4 j ^ − 2 k ^ ) = | i ^ − j ^ k ^ 2 1 2 3 4 − 2 | τ → = − 1 0 i ^ + 1 0 j ^ + 5 k ^

If force $\vec{F} = 3 \hat{i} + 4 \hat{j} - 2 \hat{k}$ acts on a particle having position vector $2 \hat{i} + \hat{j} + 2 \hat{k}$ then, the torque about the origin will be:

Option 1 - <math> <mrow> <mn>3</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <mn>4</mn> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> <mo>−</mo> <mn>2</mn> <mover accent="true"> <mi>k</mi> <mo>^</mo> </mover> </mrow> </math>

Option 2 - <math> <mrow> <mo>−</mo> <mn>1</mn> <mn>0</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <mn>1</mn> <mn>0</mn> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> <mo>+</mo> <mn>5</mn> <mover accent="true"> <mi>k</mi> <mo>^</mo> </mover> </mrow> </math>

Option 3 - <math> <mrow> <mn>1</mn> <mn>0</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <mn>5</mn> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> <mo>−</mo> <mn>1</mn> <mn>0</mn> <mover accent="true"> <mi>k</mi> <mo>^</mo> </mover> </mrow> </math>

Option 4 - <math> <mrow> <mn>1</mn> <mn>0</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> <mo>−</mo> <mn>5</mn> <mover accent="true"> <mi>k</mi> <mo>^</mo> </mover> </mrow> </math>

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Vishal Baghel | Contributor-Level 10

6 months ago

Correct Option - 2

Detailed Solution:

^{$\vec{r} = 2 \hat{i} + \hat{j} + 2 \hat{k}$}

^{$\vec{τ} = \vec{r} * \vec{F}$}

^{$= (2 \hat{i} + \hat{j} + 2 \hat{k}) * (3 \hat{i} + 4 \hat{j} - 2 \hat{k}) = | \begin{matrix} \hat{i} & - \hat{j} & \hat{k} \\ 2 & 1 & 2 \\ 3 & 4 & - 2 \end{matrix} |$}