A 50 mm diameter solid shaft is welded to a flat plate all around by fillet weld of 4mm leg size as shown in Fig. If the allowable shear strength of the weld material is 100 MPa, the maximum approximate torque in Nm that the welded joint can sustain under pure torsion is

Correct option is A

​$${\textbf{Given:}} \\\text{Diameter of shaft } d = 50\, \text{mm} \\\text{Weld size (leg size) } a = 4\, \text{mm} \\\text{Allowable shear stress } \tau_{\text{allow}} = 100\, \text{MPa} \\\text{Throat thickness of weld } = a \cdot 0.707 \\\\{\textbf{Effective Weld Area (Throat Area)}} \\\text{The throat of a fillet weld resists torsional shear. For a circular weld:} \\\text{Mean radius of the weld } R = \frac{d}{2} = 25\, \text{mm} \\\\\text{Total polar section modulus of the weld throat resisting torsion is:} \\Z_p = A_{\text{throat}} \cdot R = \left(2\pi R \cdot a \cdot 0.707\right) \cdot R = 2\pi R^2 \cdot a \cdot 0.707 \\\\\text{Substitute:} \\R = 25, \quad a = 4 \\Z_p = 2\pi (25)^2 \cdot 4 \cdot 0.707 = 2\pi \cdot 625 \cdot 4 \cdot 0.707 \\= 2\pi \cdot 2500 \cdot 0.707 \approx 6.2832 \cdot 2500 \cdot 0.707 \\\approx 15707.96 \cdot 0.707 \approx \boxed{11110\, \text{mm}^3} \\\\{\textbf{Torsional Strength}} \\T = \tau_{\text{allow}} \cdot Z_p = 100\, \text{MPa} \cdot 11110\, \text{mm}^3 \\= 1.111 \times 10^6\, \text{Nmm} = \boxed{1111\, \text{Nm}}$$​​