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Two particles having mass 'M' and 'm' are moving in a circular path having radius R and r respectively. If their time periods are same then the ratio of angular velocity will be : -
A
$\dfrac{r}{R}$
B
$\dfrac{R}{r}$
C
1
D
$\sqrt{\dfrac{R}{r}}$
Detailed Solution
Angular velocity: $\omega = \dfrac{2\pi}{T}$
It depends only on the time period, not on the mass or the radius.
Both particles have the same time period T, so $\omega_1 = \omega_2$.
$\dfrac{\omega_1}{\omega_2} = 1$
(Their linear speeds $v = \omega r$ are different, in the ratio R : r.)
It depends only on the time period, not on the mass or the radius.
Both particles have the same time period T, so $\omega_1 = \omega_2$.
$\dfrac{\omega_1}{\omega_2} = 1$
(Their linear speeds $v = \omega r$ are different, in the ratio R : r.)