Question

Two solid circular shafts of radii $R_1$ and $R_2$ are subjected to same torque. The maximum shear stesses developed in the two shafts are ${\tau }_1$ and ${\tau }_2$. If $\frac{R_1}{R_2}=2$, then $\frac{{\tau }_2}{{\tau }_1}$ is

Answer 1

${\tau }_{max}=\frac{2T}{\pi R^3}\frac{{\tau }_2}{{\tau }_1}={\left(\frac{R_1}{R_2}\right)}^3=(2{)}^3=8$ $(\because T_1=T_2=T)$