Question

A purse at radius 2.00 m and a wallet at radius 3.00 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is (2.00 m/ $s^2$)$\hat{i}$ + (4.00 m/ $s^2$)$\hat{j}$ . At that instant and in unit-vector notation, what is the acceleration of the wallet? IIT JEE- 2001

• A. 2 $\hat{i}$ + 4 $\hat{j}$
• B. 4 $\hat{i}$ + 2 $\hat{j}$
• C. 3 $\hat{i}$ + 6 $\hat{j}$
• D. 3 $\sqrt{5}$ $\hat{i}$ + 3 $\sqrt{5}$ $\hat{j}$

Answer 1

The correct option is C

3 $\hat{i}$ + 6 $\hat{j}$

$\frac{d\theta }{dt}$ is constant.

In other words in uniform circular motion the angular velocity remains constant body doesn't have any tangential acceleration but normal acceleartion.

$a_N=\frac{v^2}{R}or{\omega }^{2}R$
$Forpurse{a}_N=\sqrt{(2{)}^2+(4{)}^2}=\sqrt{20};R=2$
$\Rightarrow \sqrt{20}={\omega }^{2}2$
$\Rightarrow {\omega }^2=\sqrt{5}$
$Forwallet{a}_N={\omega }^{2}R$
Hence $\omega$is same
But~R=3
$\Rightarrow a_N=\sqrt{5}\times 3$
$a_N=3\sqrt{5}$

So the above answer matches with the magnitude of third option in the given answers.