Correct Answer - Option 3 : 117.57 mm

**Concept:**

**Stress: **Internal resistance offered by the material to the deformation given by,

\(σ = \frac {F}{A}\)

Where, **F** = Force, **A** = Area

**Calculation:**

**Given:**

D_{i} = 100 mm = 0.1 m, F = 300 KN = 300000 N, σ = 100 MN/m2 = 10^{8} N/m2, D_{o} = ?

Area, A = \(\frac{\pi}{4(D^2_o-D^2_i)}=\frac{\pi}{4(D^2_o-0.1^2)}\)

Using \(σ = \frac {F}{A}\)

\(10^8 = \frac {4\times 300000}{\pi (D_o ^2 \ -\ 0.1^2)}\)

\(D_o ^2 = 0.00382 + 0.01\)

Do = \(\sqrt{0.01382}\)

Do =0.11757 m

**Do = 117.57 mm**