A torque T is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is G. The expression for diameter ‘d’ to produce an angular twist q at the free end is

A

$$\left(\frac{30 TL}{\pi \theta G}\right)^{\frac{1}{4}}$$

B

$$\left(\frac{33 TL}{\pi \theta G}\right)^{\frac{1}{4}}$$

C

$$\left(\frac{18 TL}{\pi \theta G}\right)^{\frac{1}{4}}$$

D

$$\left(\frac{24 TL}{\pi \theta G}\right)^{\frac{1}{4}}$$