1. Given data

• Diameter of wire: $d = 14\,\text{mm} = 14 \times 10^{-3}\,\text{m}$
• Radius of wire: $r = \frac{d}{2} = 7 \times 10^{-3}\,\text{m}$
• Tensile stress: $\sigma = 7 \times 10^5\,\text{N m}^{-2}$
• Acceleration due to gravity: $g = 9.8\,\text{m s}^{-2}$
• Use: $\pi = \frac{22}{7}$

2. Relation between stress and force

Tensile stress is given by: $\sigma = \frac{F}{A}$ where $F = mg$ and cross-sectional area of the wire is: $A = \pi r^2$

So, $mg = \sigma A = \sigma \pi r^2$

Hence, $m = \frac{\sigma \pi r^2}{g}$

3. Calculate area of cross-section

$A = \pi r^2 = \frac{22}{7} \times (7 \times 10^{-3})^2$ $= \frac{22}{7} \times 49 \times 10^{-6}$ $= 22 \times 7 \times 10^{-6}$ $= 154 \times 10^{-6}$ $= 1.54 \times 10^{-4}\,\text{m}^2$

4. Calculate force

$F = \sigma A = 7 \times 10^5 \times 1.54 \times 10^{-4}$ $= 7 \times 1.54 \times 10^{1}$ $= 10.78 \times 10$ $= 107.8\,\text{N}$

Thus, $mg = 107.8$

5. Calculate mass

$m = \frac{107.8}{9.8} = 11$

6. Final answer

$\boxed{11}$

The mass of the block is $11\,\text{kg}$.