A rod of mass 1 kg is kept on a frictionless | vedclass

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

Question

(C) The net force acting on the rod is $F_{net} = 6 \ N + 3 \ N = 9 \ N$.To find the position of the equivalent single force,we calculate the net torq

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(C) The net force acting on the rod is $F_{net} = 6 \ N + 3 \ N = 9 \ N$.To find the position of the equivalent single force,we calculate the net torque about the center $C$ of the rod.Taking clockwise torque as positive,the torque due to the $6 \ N$ force is $	au_1 = 6 \ N 	imes 2 \ m = 12 \ N \cdot m$.The torque due to the $3 \ N$ force is $	au_2 = -3 \ N 	imes 1 \ m = -3 \ N \cdot m$ (counter-clockwise).The net torque is $	au_{net} = 12 - 3 = 9 \ N \cdot m$.For a single force $F_{net}$ to have the same effect,it must produce the same net torque about the center $C$ at a distance $x$:$	au_{net} = F_{net} 	imes x$$9 \ N \cdot m = 9 \ N 	imes x$$x = 1 \ m$.

$A$ rod of mass $1 \ kg$ is kept on a frictionless table and is acted upon by $2$ forces as shown. We want to replace these $2$ forces by a single force so that the effect on the rod is the same. At what distance $x$ (in $m$) from the center $C$ of the rod should we apply this single force?

Similar Questions

Which forces are needed for the rotational motion about a fixed axis?

The center of an equilateral triangle $ABC$ is $O$. Three forces $F_1$,$F_2$,and $F_3$ are applied along the sides $AB$,$BC$,and $AC$ respectively. If the total torque about $O$ is zero,what is the relationship between $F_1$,$F_2$,and $F_3$?

The torque of a force $\overrightarrow{F} = -3\hat{i} + \hat{j} + 5\hat{k}$ acting at the point $\overrightarrow{r} = 7\hat{i} + 3\hat{j} + \hat{k}$ is:

$A$ 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 ............. $N m$.

The torque due to the force $\vec{F} = (2 \hat{i} + \hat{j} + 2 \hat{k})$ about the origin,acting on a particle whose position vector is $\vec{r} = (\hat{i} + \hat{j} + \hat{k})$,is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module