Question

what is the gear ratio of this compound gear train? * 24 12 84 6 1:26 1:28 28:1 26:1

Explanation:

Step1: Calculate gear - ratio of first pair

The gear - ratio of two meshing gears is the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear. For the first pair of gears with 24 and 12 teeth, the gear - ratio $r_1=\frac{12}{24}=\frac{1}{2}$.

Step2: Calculate gear - ratio of second pair

For the second pair of gears with 84 and 6 teeth, the gear - ratio $r_2=\frac{84}{6}=14$.

Step3: Calculate overall gear - ratio

The overall gear - ratio $R$ of a compound gear train is the product of the gear - ratios of each pair. So $R = r_1\times r_2=\frac{1}{2}\times14 = 7$. But if we consider the order of input and output in terms of the problem's perspective (assuming the 24 - tooth gear is the input and 6 - tooth gear is the output), we take the reciprocal of the product of the ratios of the pairs in reverse - order. The overall gear - ratio $R=\frac{24}{12}\times\frac{6}{84}=\frac{1}{7}\times4=\frac{4}{7}
eq7$. The correct way is to consider the product of the ratios of the driving - to - driven teeth ratios. The overall gear - ratio $R=\frac{24}{12}\times\frac{84}{6}=\frac{24\times84}{12\times6}=28$. So the gear ratio is $28:1$.

Answer:

C. 28:1