A force of (2hat i - 4hat j + 2hat k) N acts | vedclass

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(B) Given: Force $\overrightarrow{F} = (2\hat{i} - 4\hat{j} + 2\hat{k}) \ N$ and position vector $\overrightarrow{r} = (3\hat{i} + 2\hat{j} - 4\hat{k}

Vedclass · Accepted Answer

$24.4$

Vedclass · Answer

(B) Given: Force $\overrightarrow{F} = (2\hat{i} - 4\hat{j} + 2\hat{k}) \ N$ and position vector $\overrightarrow{r} = (3\hat{i} + 2\hat{j} - 4\hat{k}) \ m$.The torque $\overrightarrow{	au}$ is given by the cross product $\overrightarrow{r} 	imes \overrightarrow{F}$:$\overrightarrow{	au} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 3 & 2 & -4 \ 2 & -4 & 2 \end{vmatrix}$Expanding the determinant:$\overrightarrow{	au} = \hat{i}(2 	imes 2 - (-4) 	imes (-4)) - \hat{j}(3 	imes 2 - (-4) 	imes 2) + \hat{k}(3 	imes (-4) - 2 	imes 2)$$\overrightarrow{	au} = \hat{i}(4 - 16) - \hat{j}(6 + 8) + \hat{k}(-12 - 4)$$\overrightarrow{	au} = -12\hat{i} - 14\hat{j} - 16\hat{k} \ N-m$The magnitude of torque is $|\overrightarrow{	au}| = \sqrt{(-12)^2 + (-14)^2 + (-16)^2}$$|\overrightarrow{	au}| = \sqrt{144 + 196 + 256} = \sqrt{596} \approx 24.41 \ N-m$.Thus,the correct option is $B$.

$A$ force of $(2\hat i - 4\hat j + 2\hat k) \ N$ acts at a point $(3\hat i + 2\hat j - 4\hat k) \ m$ from the origin. The magnitude of torque is ......... $N-m$.

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