If force <math> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <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> <math><mrow><mover accent="true"><mrow></mrow></mover><mover accent="true"></mover><mover accent="true"></mover><mover accent="true"></mover></mrow></math> acts on a particle having position vector <math> <mrow> <mn>2</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <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> <math><mrow><mover accent="true"></mover><mover accent="true"></mover><mover accent="true"></mover></mrow></math> 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 <math> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <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> <math><mrow><mover accent="true"><mrow></mrow></mover><mover accent="true"></mover><mover accent="true"></mover><mover accent="true"></mover></mrow></math>&nbsp;acts on a particle having position vector <math> <mrow> <mn>2</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <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> <math><mrow><mover accent="true"></mover><mover accent="true"></mover><mover accent="true"></mover></mrow></math>&nbsp;then, the torque about the origin will be:

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Overview Physics Laws of Motion Physics Class 11th

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 -

$3 \hat{i} + 4 \hat{j} - 2 \hat{k}$

Option 2 -

$- 10 \hat{i} + 10 \hat{j} + 5 \hat{k}$

Option 3 -

$10 \hat{i} + 5 \hat{j} - 10 \hat{k}$

Option 4 -

$10 \hat{i} + \hat{j} - 5 \hat{k}$

2 Views | Posted 3 weeks ago

Asked by Shiksha User

1 Answer

Answered by

Raj Pandey | Contributor-Level 9

3 weeks ago

Correct Option - 2

Detailed Solution:

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

$\vec{τ} = \vec{r} \times \vec{F}$

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

$\vec{τ} = - 10 \hat{i} + 10 \hat{j} + 5 \hat{k}$

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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:

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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:

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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: