A particle of mass m moves with a constant ve | vedclass

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

Question

(D) The angular momentum of a particle about an origin $O$ is given by $\vec{L} = \vec{r} 	imes \vec{p} = m(\vec{r} 	imes \vec{v})$. The magnitude i

Vedclass · Accepted Answer

It increases as it moves towards the line $BC$.

Vedclass · Answer

(D) The angular momentum of a particle about an origin $O$ is given by $\vec{L} = \vec{r} 	imes \vec{p} = m(\vec{r} 	imes \vec{v})$. The magnitude is $L = mvr \sin 	heta = mv d$,where $d$ is the perpendicular distance from the origin to the line of motion.$1$. For motion along $OA$,the line of motion passes through the origin $O$,so $d = 0$ and $L = 0$. Statement $A$ is correct.$2$. For the line $DE$,the perpendicular distance from $O$ to the line $DE$ is constant $(1 \ m)$. Thus,$L$ is constant at all points on $DE$. Statement $B$ is correct.$3$. At $B$,the perpendicular distance is $1 \ m$ and the velocity is in the $+y$ direction. At $D$,the perpendicular distance is $1 \ m$ and the velocity is in the $+x$ direction. The angular momentum is a vector quantity. The direction of $\vec{L}$ at $B$ is $\vec{r} 	imes \vec{v} = (1\hat{i}) 	imes (v\hat{j}) = mv\hat{k}$. The direction of $\vec{L}$ at $D$ is $\vec{r} 	imes \vec{v} = (1\hat{j}) 	imes (v\hat{i}) = -mv\hat{k}$. Thus,they have the same magnitude but opposite directions. Statement $C$ is correct.$4$. As the particle moves towards the line $BC$,the perpendicular distance $d$ from the origin $O$ to the line of motion remains constant. Therefore,the angular momentum does not change. Statement $D$ is incorrect.

$A$ particle of mass $m$ moves with a constant velocity. Which of the following statements is incorrect regarding its angular momentum?

Similar Questions

$A$ particle having mass $4 \ kg$ is moving with velocity $(4 \hat{i} + 2 \hat{j}) \ m/s$. Find the angular momentum of the particle about the origin when it is at position $(1, 1, 0) \ m$.

The angular momentum of a body is the product of which of the following?

Two particles,each of mass $m$ and speed $v$,travel in opposite directions along parallel lines separated by a distance $d$. Show that the angular momentum vector of the two-particle system is the same whatever be the point about which the angular momentum is taken.

Can an object moving in a straight line have angular momentum?

Vedclass Test Series

Exam Paper Generator

Online Exam Module