A solid cone hangs from a frictionless pivot | vedclass

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

Question

(C) The torque is given by $\vec{	au} = \vec{r} 	imes \vec{F}$.For option $A$: $\vec{r} = b \hat{j} - c \hat{k}$ and $\vec{F} = a \hat{k}$.$\vec{	a

Vedclass · Accepted Answer

$F = a \hat{j}$,$P$ is $(-b, 0, -c)$

Vedclass · Answer

(C) The torque is given by $\vec{	au} = \vec{r} 	imes \vec{F}$.For option $A$: $\vec{r} = b \hat{j} - c \hat{k}$ and $\vec{F} = a \hat{k}$.$\vec{	au} = (b \hat{j} - c \hat{k}) 	imes (a \hat{k}) = ab(\hat{j} 	imes \hat{k}) - ac(\hat{k} 	imes \hat{k}) = ab \hat{i}$. The $z$-component is $0$.For option $B$: $\vec{r} = -b \hat{j} - c \hat{k}$ and $\vec{F} = -a \hat{k}$.$\vec{	au} = (-b \hat{j} - c \hat{k}) 	imes (-a \hat{k}) = ab(\hat{j} 	imes \hat{k}) + ac(\hat{k} 	imes \hat{k}) = ab \hat{i}$. The $z$-component is $0$.For option $C$: $\vec{r} = -b \hat{i} - c \hat{k}$ and $\vec{F} = a \hat{j}$.$\vec{	au} = (-b \hat{i} - c \hat{k}) 	imes (a \hat{j}) = -ab(\hat{i} 	imes \hat{j}) - ac(\hat{k} 	imes \hat{j}) = -ab \hat{k} - ac(-\hat{i}) = ac \hat{i} - ab \hat{k}$.The $z$-component is $-ab$,which is negative since $a, b > 0$.

Similar Questions

If force $\vec{F} = -3 \hat{i} + \hat{j} + 5 \hat{k}$ acts at a position vector $\vec{r} = 7 \hat{i} + 3 \hat{j} + \hat{k}$,then the torque $\vec{\tau}$ acting at that point is:

$A$ wheel of radius $R$ with an axle of radius $R/2$ is shown in the figure and is free to rotate about a frictionless axis through its centre and perpendicular to the page. Three forces are exerted as shown in the figure. The magnitude of the net torque acting on the system is nearly (in $FR$)

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:

$A$ 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?

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module