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

Answer:

C) 1200 rpm

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.

$\frac{N_1}{N_2}=\frac{D_2}{D_1}\\\Rightarrow \frac{400}{N_2}=\frac{8}{24}\\\Rightarrow N_2=\frac{24\times 400}{8}\\\Rightarrow N_2=1200\ rpm$

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