The solid shaft $\backslash ($ A E $\backslash )$ rotates at $600$ rpm and transmits $60$ hp from the motor $\backslash ($ M $\backslash )$ to machine tools connected to gears $\backslash ($ G $\backslash )$ and $\backslash ($ H $\backslash ).$ Knowing that $\backslash ($ T$\_\{\backslash$text $\{$all $\}\}=7\mathrm{.}6\backslash$mathrm$\{$ksi$\}\backslash )$ and that $40$ hp is taken off at gear $\backslash ($ G $\backslash )$ and $20$ hp is taken off at gear H $,$ determine the smallest permissible diameter of shaft $\backslash ($ A E $\backslash ).($Round the final answer to three decimal places.$)$

The smallest permissible diameter of shaft $\backslash ($ A E $\backslash )$ is

in$.$