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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 ...?

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Answer:

C) 1200 rpm

Explanation:

[tex]D_1[/tex] = Diameter of bigger pulley = 24 inch

[tex]D_2[/tex] = Diameter of smaller pulley = 8 inch

[tex]N_1[/tex] = Speed of bigger pulley = 400 rpm

[tex]N_2[/tex] = Speed of smaller pulley

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

[tex]\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[/tex]

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

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