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3-2.Motion in Plane
easy
A car is going round a circle of radius $R_1$ with constant speed. Another car is going round a circle of radius $R_2$ with constant speed. If both of them take same time to complete the circles, the ratio of their angular speeds and linear speeds will be .........
A$\sqrt{\frac{R_1}{R_2}}, \frac{R_1}{R_2}$
B$1, 1$
C$1, \frac{R_1}{R_2}$
D$\frac{R_1}{R_2}, 1$
Solution
(c)
The angular speed is given by $\omega=\frac{2 \pi}{T}$
$\omega \propto \frac{1}{T} \Rightarrow \frac{\omega_1}{\omega_2}=\frac{T_2}{T_1}$
if $T_1=T_2 \Rightarrow \omega_1=\omega_2$
So, ratio $\Rightarrow 1: 1$
and linear speed $v=R \omega$
$V \propto R$
$\frac{V_1}{V_2}=\frac{R_1}{R_2}$
The angular speed is given by $\omega=\frac{2 \pi}{T}$
$\omega \propto \frac{1}{T} \Rightarrow \frac{\omega_1}{\omega_2}=\frac{T_2}{T_1}$
if $T_1=T_2 \Rightarrow \omega_1=\omega_2$
So, ratio $\Rightarrow 1: 1$
and linear speed $v=R \omega$
$V \propto R$
$\frac{V_1}{V_2}=\frac{R_1}{R_2}$
Standard 11
Physics
