If a 32 tooth gear is the input gear what is the gear ratio at the rightmost 8 tooth gear?

• A. 4:1
• B. 3:1
• C. 2:1
• D. 8:1

Answer: (B)

When gears mesh, the tangential speed at the contact point is the same for both gears. That means the angular velocity of the next gear is scaled by the ratio of the teeth counts: ω_next = ω_previous × (N_previous / N_next). In a train, this effect cascades, but the intermediate gears cancel out, so the overall ratio from the first gear to the last gear depends only on their tooth counts.

Here, the input gear has 32 teeth and the rightmost gear has 8 teeth. The output speed is ω_out = ω_in × (32 / 8) = ω_in × 4. So the reduction ratio (input:output speed) is 4:1, and the rightmost gear turns at one-quarter the speed of the input. The other given ratios don’t match this calculation.