Question

When a disc is rotating with angular velocity $ \omega $ , a particle situated at a distance of $ 4 \,cm $ just begins to slip. If the angular velocity is doubled, at what distance will the particle start to slip?

• A. $ 1 \,cm $
• B. $ 2 \,cm $
• C. $ 3 \,cm $
• D. $ 4 \,cm $

Answer 1

Answer: (A)

Angular velocity $=\omega$
Centripetal force $F=m r \omega^{2}$
Or $\,\,\,r \propto \frac{1}{\omega^{2}}$
$\therefore \frac{r_{1}}{r_{2}}=\frac{\omega_{2}^{2}}{\omega_{1}^{2}} $
or $ \frac{4}{r_{2}}=\frac{4 \omega^{2}}{\omega^{2}}$
or $r_{2}=1 \,cm$