Question

The gear A of 20 teeth meshes with gear B of 10 teeth that is compounded to wheel C of 30 teeth that meshes with gear D of 10 teeth. The velocity ratio between gear D and gear A is

• A. 3
• B. 5
• C. 4
• D. 6

Hint:

For a series of meshing gears, multiply the individual gear ratios to find the overall velocity ratio. For compounded gears, the speeds are the same.

Answer 1

The Correct Option is D

Step 1: Understanding Gear Ratios: When two gears mesh, their speed ratio is inversely proportional to their number of teeth. That is: \[ \frac{\text{Speed of Gear 1}}{\text{Speed of Gear 2}} = \frac{\text{Number of Teeth on Gear 2}}{\text{Number of Teeth on Gear 1}} \]
Step 2: Calculating Intermediate Speeds: Gear A and Gear B: \( \frac{\text{Speed of B}}{\text{Speed of A}} = \frac{20}{10} = 2 \). So, gear B rotates twice as fast as gear A. Gear B and Gear C: Gears B and C are compounded, meaning they are on the same shaft and rotate at the same speed. Therefore, Speed of C = Speed of B. Gear C and Gear D: \( \frac{\text{Speed of D}}{\text{Speed of C}} = \frac{30}{10} = 3 \). So, gear D rotates three times as fast as gear C.
Step 3: Calculating Overall Velocity Ratio (D to A): \[ \frac{\text{Speed of D}}{\text{Speed of A}} = \frac{\text{Speed of D}}{\text{Speed of C}} \times \frac{\text{Speed of C}}{\text{Speed of B}} \times \frac{\text{Speed of B}}{\text{Speed of A}} \] Since Speed of C = Speed of B: \[ \frac{\text{Speed of D}}{\text{Speed of A}} = 3 \times 1 \times 2 = 6 \]