Question

Velocity ratio for pulley drive is given by [Where D₁ = diameter of driving pulley, D₂ = diameter of driven pulley, t = thickness of belt, S = total percentage slip]
1. \(\left( {\frac{{{D_1} + t}}{{{D_2} + t}}} \right)\left( {\frac{{100 + S}}{S}} \right)\)
2. \(\left( {\frac{{{D_1} + t}}{{{D_2} + t}}} \right)\left( {\frac{{100 - S}}{S}} \right)\)
3. \(\left( {\frac{{{D_1} + t}}{{{D_2} + t}}} \right)\left( {\frac{{100 - S}}{{100}}} \right)\)
4. \(\left( {\frac{{{D_1} + t}}{{{D_2} + t}}} \right)\left( {\frac{{100 + S}}{{100}}} \right)\)

Answer 1

Correct Answer - Option 3 : \(\left( {\frac{{{D_1} + t}}{{{D_2} + t}}} \right)\left( {\frac{{100 - S}}{{100}}} \right)\)

Explanation:

Velocity Ratio:

Velocity ratio is the ratio of the speed of the driven pulley to that of the driving pulley.

Velocity ratio = \(\frac{N_2}{N_1}=\frac{D_1\;+\;t}{D_2\;+\;t}\)

where D and t represent diameter and thickness respectively.

In the case of belt drive where the slip (S) is present the velocity ratio is given by:

Velocity ratio = \(\frac{N_2}{N_1}=\frac{D_1\;+\;t}{D_2\;+\;t}\left ( \frac{100\;-\;S}{100} \right )\)

In gear and chain drive velocity ratio is given by:

Velocity ratio = \(\frac{N_2}{N_1}=\frac{D_1}{D_2}\)

∵ slip is absent and thickness is very less as compared to the diameter so it can be ignored, ∴ it is constant.