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.A) 133 1/3B) 800C) 1,200 ...?

Answer 1

C) 1200 rpm

Step-by-step explanation:

`D_1` = Diameter of bigger pulley = 24 inch

`D_2` = Diameter of smaller pulley = 8 inch

`N_1` = Speed of bigger pulley = 400 rpm

`N_2` = Speed of smaller pulley

The relation between revolutions per minute and diameter is that they are inversely proportional.

`(N_1)/(N_2)=(D_2)/(D_1)\\\Rightarrow (400)/(N_2)=(8)/(24)\\\Rightarrow N_2=(24* 400)/(8)\\\Rightarrow N_2=1200\ rpm`

The number of revolutions per minute of the smaller pulley is 1200 rpm