Question

Two cars of masses $m_{1}$ , and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$, respectively. Their speeds are such that they make complete circles in the same time $t$. The ratio of their centripetal acceleration is

• A. $m_{1}r_{1} : m_{2}r_{2}$
• B. $m_{1}: m_{2}$
• C. $r_{1} : r_{2}$
• D. $ 1 : 1$

Answer 1

Answer: (C)

Centripetal acceleration, $a_{e}=\omega^{2}r$
Angular velocity , $\omega=\frac{2 \pi}{T}$
The cars make complete circle in same time.
As $T_{1}=T_{2}$
$\Rightarrow \omega_{1}=\omega_{2}$
$\therefore \frac{a_{c_1}}{a_{c_2}}=\frac{r_{1}}{r_{2}}$