91Ó°ÊÓ

1. The radius of the purse is$r_p=2.00m$
2. The radius of the wallet is$r_w=3.00m$

1. The acceleration of the purse is, $a=(2.00m/s^2)\hat{i}+(4.00m/s^2)\hat{j}$

A purse and wallet travel in a uniform circular motion. They are on the same radial line; hence the angular frequency of the purse and wallet is the same. Both have centripetal acceleration only.

Formula:

$a={\mathrm{Ó\neg }}^{2}r$

The purse and the wallet are performing uniform circular motion. The radius of purse -${\mathrm{r}}_{\mathrm{P}}$and radius of the wallet -$r_w$are acting along the same line; hence their angular velocity isthesame.

The equation of acceleration of purse is

$a_P={\mathrm{Ó\neg }}^2{r}_P$ …(¾±)

The equation of acceleration of wallet is

$a_w={\mathrm{Ó\neg }}^2{r}_w$ …(¾±¾±)

Dividing equation (ii) by (i),

$$\begin{gathered} \frac{a_w}{a_p}=\frac{r_w}{r_p} \\ {a}_w=\frac{r_w}{r_p}{a}_w \\ \stackrel{→}{a_w}=\frac{3}{2}\left(\right(2.00m/s^2)\hat{i}+(4.00m/s^2\left)\hat{j}\right) \\ =(3.00m/s^2)\hat{i}+(6.00m/s^2)\hat{j} \end{gathered}$$

Therefore, the acceleration of the wallet is $(3.00m/s^2)\hat{i}+(6.00m/s^2)\hat{j}$.