Question

what is the gear ratio of this compound gear train? * 1 point 84 60 24 1:2 1:36 10:49 12:87

Explanation:

Step1: Recall gear - ratio formula for compound gear train

The gear ratio \(G\) of a compound gear train is given by the product of the ratios of the number of teeth of the driving gears to the number of teeth of the driven gears. If we assume the left - most gear as the driving gear and the right - most gear as the driven gear, and the middle compound gear has two sets of teeth. The ratio of the first stage is \(\frac{N_1}{N_2}\) and the ratio of the second stage is \(\frac{N_3}{N_4}\), and the overall gear ratio \(G=\frac{N_1}{N_2}\times\frac{N_3}{N_4}\). Here, \(N_1 = 84\), \(N_2=60\), \(N_3 = 84\), \(N_4 = 24\).

Step2: Calculate the gear ratio

\[

$$\begin{align*} G&=\frac{84}{60}\times\frac{84}{24}\\ &=\frac{7}{5}\times\frac{7}{2}\\ &=\frac{49}{10} \end{align*}$$

\]
The inverse gear ratio (driven to driving) is \(\frac{10}{49}\), which is \(10:49\).

Answer:

10:49