Oilers/Plant Tenders (HHC) Civil Service Practice Exam

If an 8" diameter pulley is driven by a 12" diameter pulley (which rotates at 100 rpm), what will be the rpm of the driven pulley?

1. 100 rpm

2. 150 rpm

3. 75 rpm

4. 120 rpm

The correct answer is: 150 rpm

To determine the rpm of the driven pulley, we can use the relationship between the diameters of the pulleys and their rotational speeds. The key principle here is that the linear speed at the circumference of both pulleys must be equal since they are connected. First, let's denote the diameter and rpm of the driving pulley (the larger one) and the driven pulley (the smaller one): - Diameter of the driving pulley (D1) = 12 inches - Diameter of the driven pulley (D2) = 8 inches - RPM of the driving pulley (N1) = 100 The linear speed (v) at the edge of a pulley is given by the formula: \[ v = \pi \times D \times N \] Where: - \( v \) is the linear speed, - \( D \) is the diameter of the pulley, and - \( N \) is the rpm of the pulley. Since the linear speeds of both pulleys must be equal, we have: \[ \pi \times D1 \times N1 = \pi \times D2 \times N2 \] The \(\pi\) cancels out from both sides, which gives us: \[ D1 \