$4.$ A propeller shaft of solid circular cross section and diameter $\backslash ($ d $\backslash )$ is spliced by a collar of the same material $($see figure$).$ The collar is securely bonded to both parts of the shaft. What should be the minimum outer diameter $\backslash ($ d$\_\{1\}\backslash )$ of the collar in order that the splice can transmit the same power as the solid shaft? $(10$ pts $)$