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

A

$$P \propto (Nd^3)$$

B

$$P \propto (Nd^3)^{\frac{1}{2}}$$

C

$$P \propto (Nd^3)^{\frac{2}{3}}$$

D

$$P \propto (Nd^3)^{\frac{1}{3}}$$