A force of -F hat{k} acts on O,the origin of | 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 origin $O(0, 0)$ with respect to the point $P(1, -1)$ is given by $\vec{r} = (0 - 1)\hat{i} + (0 - (-1))\hat{

Vedclass · Accepted Answer

$-F(\hat{i}+\hat{j})$

Vedclass · Answer

(D) The position vector $\vec{r}$ of the origin $O(0, 0)$ with respect to the point $P(1, -1)$ is given by $\vec{r} = (0 - 1)\hat{i} + (0 - (-1))\hat{j} = -\hat{i} + \hat{j}$.The force acting at the origin is $\vec{F} = -F\hat{k}$.The torque $\vec{	au}$ about the point $P$ is defined as $\vec{	au} = \vec{r} 	imes \vec{F}$.Substituting the values,we get $\vec{	au} = (-\hat{i} + \hat{j}) 	imes (-F\hat{k})$.Using the cross product rules $\hat{i} 	imes \hat{k} = -\hat{j}$ and $\hat{j} 	imes \hat{k} = \hat{i}$,we have:$\vec{	au} = F(\hat{i} 	imes \hat{k}) - F(\hat{j} 	imes \hat{k})$$\vec{	au} = F(-\hat{j}) - F(\hat{i})$$\vec{	au} = -F(\hat{i} + \hat{j})$.

$A$ force of $-F \hat{k}$ acts on $O$,the origin of the coordinate system. The torque about the point $(1, -1)$ is

Similar Questions

If $\vec{F} = (5 \hat{i} - 10 \hat{j}) \text{ N}$ and $\vec{r} = (4 \hat{i} - 3 \hat{j}) \text{ m}$,then the torque $\vec{\tau}$ acting on the object will be:

Show that the moment of a couple does not depend on the point about which you take the moments.

Find the torque of a force $\vec F = -3\hat i + \hat j + 5\hat k$ acting at the point $\vec r = 7\hat i + 3\hat j + \hat k$ with respect to the origin.

$A$ slab is subjected to two forces $\vec F_1$ and $\vec F_2$ of the same magnitude $F$ as shown in the figure. Force $\vec F_2$ is in the $XY$-plane,while force $\vec F_1$ acts along the $z$-axis at the point $(2\hat i + 3\hat j)$. The moment of these forces about point $O$ is:

The torque of force $\vec F = -2\hat i + 2\hat j + 3\hat k$ acting on a point $\vec r = \hat i - 2\hat j + \hat k$ about the origin will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module