A force vec{F}=(2 hat{i}+3 hat{j}-5 hat{k}) , | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The position vector $\vec{r}$ of the point of application relative to the point about which torque is calculated is given by $\vec{r} = \vec{r}_1

Vedclass · Accepted Answer

$(13 \hat{j}-22 \hat{i}-\hat{k}) \, N m$

Vedclass · Answer

(D) The position vector $\vec{r}$ of the point of application relative to the point about which torque is calculated is given by $\vec{r} = \vec{r}_1 - \vec{r}_2$.$\vec{r} = (2 \hat{i} + 4 \hat{j} + 7 \hat{k}) - (\hat{i} + 2 \hat{j} + 3 \hat{k}) = \hat{i} + 2 \hat{j} + 4 \hat{k} \, m$.The torque $\vec{	au}$ is defined as $\vec{	au} = \vec{r} 	imes \vec{F}$.$\vec{	au} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & 2 & 4 \ 2 & 3 & -5 \end{vmatrix}$.Calculating the determinant: $\vec{	au} = \hat{i} [ (2)(-5) - (4)(3) ] - \hat{j} [ (1)(-5) - (4)(2) ] + \hat{k} [ (1)(3) - (2)(2) ]$.$\vec{	au} = \hat{i} [ -10 - 12 ] - \hat{j} [ -5 - 8 ] + \hat{k} [ 3 - 4 ]$.$\vec{	au} = -22 \hat{i} + 13 \hat{j} - \hat{k} \, N m$.

$A$ force $\vec{F}=(2 \hat{i}+3 \hat{j}-5 \hat{k}) \, N$ acts at a point $\vec{r}_1=(2 \hat{i}+4 \hat{j}+7 \hat{k}) \, m$. The torque of the force about the point $\vec{r}_2=(\hat{i}+2 \hat{j}+3 \hat{k}) \, m$ is ............. $N m$.

Similar Questions

The force $\vec{F} = 7\hat{i} + 3\hat{j} - 5\hat{k}$ acts on a particle whose position vector is $\vec{r} = \hat{i} - \hat{j} + \hat{k}$. What is the torque of the given force about the origin?

$A$ triangular plate is shown in the figure. $A$ force $\overrightarrow{F} = 4 \hat{i} - 3 \hat{j}$ is applied at point $P$. The torques at point $P$ with respect to point $O$ and point $Q$ are:

What is the torque of the force $\vec{F} = (2\hat{i} - 3\hat{j} + 4\hat{k}) \text{ N}$ acting at the point $\vec{r} = (3\hat{i} + 2\hat{j} + 3\hat{k}) \text{ m}$ about the origin?

The vector sum of a system of non-collinear forces acting on a rigid body is given to be nonzero. If the vector sum of all the torques due to the system of forces about a certain point is found to be zero,does this mean that it is necessarily zero about any arbitrary point?

Vedclass Test Series

Exam Paper Generator

Online Exam Module