A thick cylinder of inner dia ‘D’, wall thickness $$t_2$$ and length ‘L’ is sealed at its both ends with caps. The thickness of the cap is $$t_1$$. Allowable tensile yield stress = $$\sigma_y$$ and allowable shear stress = $$\tau_y$$. A gas is pumped into this cylinder at pressure ‘p’. The cap will yield in shear at circumference of diameter ‘D’ when the gas pressure applied is more than

A

$$\frac{4 t_{1} \tau_{y}}{D}$$

B

$$\frac{8 t_{1} \tau_{y}}{D}$$

C

$$\frac{4 t_{2} \sigma_{y}}{D}$$

D

$$\frac{2 t_{1} \tau_{y}}{D}$$