$(25$ pts$)$ Two solid shafts of diameter $d$ are to be joined by a sleeve with an outer diameter of $d_1.$ The sleeve is to be glued to the shaft rather than welded. The shear strength of the glue is $$ psi. Determine the length of the shaft that should be placed into the sleeve to transmit a force $P$ for a factor of safety of $2.$

Given

$f.S=2$

$A=\frac{}{4}{d}^2$

${}_1=\frac{G_1}{A_1}$