A power transmission shaft of diameter d rotating at the speed of N rpm. The speed N is related to diameter d and P as ________.

A

$$N \propto \left(\frac{P}{d^{3}}\right)^{\frac{2}{3}}$$

B

$$N \propto \left(\frac{P}{d^{3}}\right)^{\frac{1}{2}}$$

C

$$N \propto \left(\frac{P}{d^{3}}\right)$$

D

$$N \propto \left(\frac{P}{d^{3}}\right)^{2}$$