91Ó°ÊÓ

Figure is given to rank the points according to the magnitude of the angular momentum of the particle measured about them.

Using the equation of angular momentum, rank the points according to the magnitude of the angular momentum of the particle measured about them.

The formula is as follows:

$\begin{array}{c}L=r×P\\ =rP\sin \mathrm{θ}\end{array}$

Where,$\mathrm{θ}$ is the angle between $P$and the position vector$r.$

Now,

$\begin{array}{c}L=r×P\\ =rP\sin \mathrm{θ}\end{array}$

For points a and e, the angle between the momentum vector and the distance from the moving particle to points a and e is zero. So,

From figure,$r=4$for point a andfor$r=8$point b,

$L_a=\left(4\right)\left(P\right)\sin 0=0$

$L_e=\left(8\right)\left(P\right)\sin 0=0$

For point c, the angle between the momentum vector and the position vector is${90}^0.$So,$r=\sqrt{13}$

From figure,$r=2$for point c,

$L_c=\left(2\right)\left(P\right)\sin {90}^0=2P$

For point b, the angle between the momentum vector and the position vector is ${108}^0.$So,

From figure $r=\sqrt{13}$, for point b,

$L_b=\sqrt{13}\left(P\right)\sin {108}^0=3.42P$

For point d, the angle between the momentum vector and the position vector isSo,

From figure,$r=\sqrt{13}$for point d,

$L_d=\sqrt{13}\left(P\right)\sin {33.69}^0=2P$

Therefore,

$L_b>L_c=L_d>L_a=L_e$

Hence, using the equation of angular momentum, the points can be ranked according to the magnitude of the angular momentum of the particle measured about them and the rank is,

.$L_b>L_c=L_d>L_a=L_e$