Question

A particle of mass $m$ moves with a constant velocity. Which of the following statements is not correct about its angular momentum about origin?

• A. It is zero when it is at $A$ and moving along $OA$ .
• B. It is same at all points along the line $DE$
• C. It is of the same magnitude but oppositely directed at
  $B$ and $D$ .
• D. It increases as it moves along the line $BC$ .

Answer 1

Answer: (D)

Angular momentum of a particle about a point can be given by the cross product of its position vector and the momentum vector.
$\left|\overrightarrow{L}\right|=\left|\overrightarrow{r}\times \overrightarrow{p}\right|=mvrsin\left(\theta \right)=m{v}_{\perp }r=mv{r}_{\perp }$
$\hat{L}=\hat{r}\times \hat{p}$
It simplifies to the product of distance and the tangential velocity. The direction can be given by the right hand thumb rule.
As the particle moves along $OA$ , the position vector and momentum vector are colinear so the cross product is zero.
Along $DE$ the cross product of the momentum vector and position vector always points towards out of the plane of paper.
Along $BC$ the cross product of the momentum vector and position vector always points into the plane of paper.
Along $BC$ and $DE$ the magnitude of the cross product is the same.