Question

Two cars having masses $m_{1}$ and $m_{2}$ move in circles of radii $r_{1}$ and $r_{2}$ respectively. If they complete the circles in equal time, the ratio of their angular speeds $\omega_{1} / \omega_{2}$ is

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

Answer 1

Answer: (D)

$ T_{1}=T_{2}$
$\frac{2 \pi r_{1}}{v_{1}}=\frac{2 \pi r_{2}}{v_{2}}$
$\Rightarrow \frac{v_{1}}{r_{1}}=\frac{v_{2}}{r_{2}}$
or $\omega_{1}=\omega_{2}$
$\Rightarrow \frac{\omega_{1}}{\omega_{2}}=1$