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Consider a simple gear train consisting of three gear wheels with 20, 15 and 40 teeth respectively. The velocity ratio of third wheel to first wheel would be
  • a)
    1/2 and same direction
  • b)
    1/2 and opposite direction
  • c)
    2 and same direction
  • d)
    2 and opposite direction
Correct answer is option 'A'. Can you explain this answer?
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The velocity ratio of a gear train is defined as the ratio of the angular velocity (rotational speed) of the output gear to the angular velocity of the input gear. In a gear train, the velocity ratio is determined by the number of teeth on each gear.

In this case, we have a gear train with three gears: one with 20 teeth (first gear), one with 15 teeth (second gear), and one with 40 teeth (third gear).

The velocity ratio of the third gear to the first gear can be calculated using the formula:

Velocity ratio = (Number of teeth on the second gear / Number of teeth on the first gear) * (Number of teeth on the third gear / Number of teeth on the second gear)

= (15 / 20) * (40 / 15)

= (3/4) * (8/3)

= 2

So, the velocity ratio of the third gear to the first gear is 2.

The direction of rotation can be determined by analyzing the number of teeth on each gear. In this case, the first and third gears have different numbers of teeth, which means they will rotate in opposite directions. Therefore, the correct answer is option 'A': the velocity ratio is 1/2 and the gears rotate in the same direction.

To summarize:

- The velocity ratio of the third gear to the first gear is 2.
- The gears rotate in the same direction.
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Consider a simple gear train consisting of three gear wheels with 20, 15 and 40 teeth respectively. The velocity ratio of third wheel to first wheel would bea)1/2 and same directionb)1/2 and opposite directionc)2 and same directiond)2 and opposite directionCorrect answer is option 'A'. Can you explain this answer?
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