Multiple choice

A planetary gear train has four gears and one carrier. Angular velocities of the gears are $\infty_1$,$\infty_4$,$\infty_4$ and$\infty_4$ respectively. The carrier rotates with angular velocity $\infty_4$.

What is the relation between the angular velocities of Gear 1 and Gear 4?

  1. $\begin{matrix} \ \omega_1 -\omega_5 \\ \ \omega_1 -\omega_5 \\ \end{matrix}=6$
  2. $\frac{\omega_1-\omega_5}{\omega_1\hspace{0.3cm}\omega_5}=6$
  3. $\frac{\omega_1-\omega_5}{\omega_4-\omega_5}=-\bigg(\frac{2}{3}\bigg)$
  4. $\frac{\omega_1-\omega_5}{\omega_4-\omega_5}=\frac{8}{9}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\frac{\omega_1-\omega_5}{\omega_4-\omega_5}=\frac{x}{x\times\frac{Z_1Z_3}{Z_2Z_4}}=\frac{Z_2Z_4}{Z_1Z_3}\\ \frac{\omega_1-\omega_5}{\omega_4-\omega_5}=\frac{45\times40}{15\times20}=3\times2=6$

Keep practicing — related questions