Question

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. $\frac{R_1}{R_2},1$

Answer 1

Answer: (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 $v=R\omega$
$V\propto R$
$\frac{V_1}{V_2}=\frac{R_1}{R_2}$