Question

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? a 10 rpm b 20 rpm c 60 rpm d 120 rpm

Explanation:

Step1: Calculate the speed after the first gear ratio

The first gear ratio is \(4:1\). When the input speed is \(240\) rpm, the speed after the first gear pair is \(240\div4 = 60\) rpm.

Step2: Calculate the speed after the second gear ratio

The second gear ratio is \(3:1\). Using the speed from Step1 (\(60\) rpm), the speed after the second gear pair is \(60\div3=20\) rpm.

Step3: Check the third gear ratio (no - effect as it's the last stage in terms of output)

The third gear ratio \(2:1\) is from the second - last gear to the output gear. But since we are calculating the output speed, and the previous two gear ratios have already given us the speed before the last gear pair (and the last gear pair is from the second - last to the output, but we are interested in the output speed which is after all gear reductions). In fact, if we consider the formula \(N_{output}=N_{input}\times\frac{1}{4}\times\frac{1}{3}\times\frac{1}{2}\) (where \(N\) is the speed). But if we calculate step - by - step as above (since each gear ratio reduces the speed). After two gear ratios (\(4:1\) and \(3:1\)), we get the output speed.

Answer:

B. \(20\) rpm