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 2 months ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

2 months 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: