Question

The number of revolutions of two pulleys is inversely proportional to their diameters. If a 24-inch diameter pulley making 400 revolutions per minute is belted to an 8-inch diameter pulley, find the number of revolutions per minute of the smaller pulley.

Answer 1

Number of revolution of smaller pulley of 8 inches is 1200 revolution per minute.

Solution:

Given that number of revolution of two pulleys is inversely proportional to their diameter.

Let say diameter of two pulley be
`\mathrm{d}_(1) \text { and } \mathrm{d}_(2)`

And revolution of two pulleys be
`\mathrm{r}_(1) \text { and } \mathrm{r}_(2)`

From given information
`\mathrm{d}_(1)` is inversely proportional to
`\mathrm{r}_(1)` and
`\mathrm{d}_(2)` is inversely proportional to
`\mathbf{r}_(2)`

Assuming k be constant of proportionality we get

`\mathrm{d}_(1)=(k)/(r_(1)) \text { and } d_(2)=(k)/(r_(2))`

so we get

`(d_(1))/(d_(2))=(r_(2))/(r_(1))`

Given that
`{d}_(1)` = 24 inches,
`{r}_(1)` = 400 revolution per minute ,
`{d}_(2)` = 8 inches. we need to calculate
`{r}_(2)`

`(24)/(8)=(r_(2))/(400)`

`{r}_(2) = 24 * (400)/(8)` = 1200 revolutions per minute.

Hence number of revolution of smaller pulley of 8 inches is 1200 revolution per minute.