A 42.0-cm-diameter wheel, consisting of a rim and six spokes, is constructed from a thin, rigid plastic material having a linear mass density of 25.0 g/cm. This wheel is released from rest at the top of a hill 58.0 m high. (a) How fast is it rolling when it reaches the bottom of the hill? (b) How would your answer change if the linear mass density and the diameter of the wheel were each doubled?
Solution 83P Step 1: This is the diagram which represents the wheel with six spokes and a rim. Provided, linear mass density of the wheel, = 25 g/ cm We have to convert this from g/ cm to kg / m We know that, 1 kg = 10 g and 1 m = 10 cm 2 Therefore, 1 kg/ m = 10 g / 10 cm = 10 g/ cm 1 g/cm = 10 kg / m Substituting this in equation for linear mass density, we get, -1 = 25 × 10 kg/m = 2.5 kg/m