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 circle in equal time, the ratio of their angular speeds $\frac{{\omega }_1}{{\omega }_2}$ is _______

• A. $\frac{m_1}{m_2}$
• B. $\frac{r_1}{r_2}$
• C. $\frac{m_1{r}_1}{m_2{r}_2}$
• D. 1

Answer 1

The correct option is D

1

${\omega }_1=\frac{△\theta }{△t}$

If time taken to complete a revolution is t.

Then ${\omega }_1=\frac{2\pi }{t},{\omega }_2=\frac{2\pi }{t}$

$\Rightarrow t=\frac{2\pi }{{\omega }_1}=\frac{2\pi }{{\omega }_2}$

$\Rightarrow$ we get ${\omega }_1={\omega }_{2}or\frac{{\omega }_1}{{\omega }_2}=1$