in this diagram of a simple gearbox, the gear ratios for each pair of gears is given. what will be the…

in this diagram of a simple gearbox, the gear ratios for each pair of gears is given. what will be the output speed if the input speed is 240 rpm?\na 10 rpm\nb 20 rpm\nc 60 rpm\nd 120 rpm

in this diagram of a simple gearbox, the gear ratios for each pair of gears is given. what will be the output speed if the input speed is 240 rpm?\na 10 rpm\nb 20 rpm\nc 60 rpm\nd 120 rpm

Answer

Explanation:

Step1: Calculate the overall gear - ratio

The overall gear - ratio is the product of the individual gear - ratios. Given gear - ratios of 4:1, 3:1, and 2:1. The overall gear - ratio $R = 4\times3\times2=24$.

Step2: Calculate the output speed

The formula for the relationship between input speed $N_{in}$ and output speed $N_{out}$ and gear - ratio $R$ is $N_{out}=\frac{N_{in}}{R}$. Given $N_{in} = 240$ rpm and $R = 24$. Then $N_{out}=\frac{240}{24}=10$ rpm.

Answer:

A. 10 rpm