Question

A circular tube and a square tube (as shown in figure below) are constructed of the same material. Both tubes have the same length, thickness, and cross- sectional area, and both are subjected to same torque. The ratio of the shear stress for the tubes is________

• A. 0.785

Answer 1

The correct option is A 0.785
Both tubes have area same,
So, $2\pi rt=b\times 4\times t$

$b=\frac{\pi r}{2}$

$\frac{{\tau }_1}{{\tau }_2}=\frac{\left(\frac{T}{2t{A}_{m1}}\right)}{\left(\frac{T}{2t{A}_{m2}}\right)}=\frac{A_{m2}}{A_{m1}}$

$A_m$ = Area enclosed by the median line of the cross-section

$\frac{{\tau }_1}{{\tau }_2}=\frac{b^2}{\pi r^2}=\frac{\pi }{4}$

$\frac{{\tau }_1}{{\tau }_2}=0.785$