To determine the resilience of a body, we need to calculate the strain energy stored in the body when it is subjected to an elastic deformation. Resilience is defined as the maximum strain energy per unit volume that a material can absorb without permanent deformation.

Given data:
- Volume of the body = 2 × 10^5 mm^3
- Stress (σ) = 10 N/mm^2
- Young's modulus (E) = 1 × 10^5 N/mm^2

We can calculate the strain energy using the formula:

Strain energy (U) = (1/2) * σ^2 / E

1. Conversion of units:
Since the volume is given in mm^3, we should convert it to m^3 for consistency in units. 1 mm^3 = 1 × 10^-9 m^3.
So, the volume of the body becomes 2 × 10^5 × 10^-9 m^3 = 2 × 10^-4 m^3.

Similarly, we should convert the stress and Young's modulus from N/mm^2 to N/m^2 (Pa). 1 N/mm^2 = 1 × 10^6 N/m^2.
So, the stress becomes 10 × 10^6 Pa and Young's modulus becomes 1 × 10^11 Pa.

2. Calculation of strain energy:
Substituting the values into the formula, we get:
U = (1/2) * (10 × 10^6)^2 / (1 × 10^11)
= (1/2) * 100 × 10^12 / 1 × 10^11
= (1/2) * 1000
= 500 J

3. Calculation of resilience:
Resilience is defined as the maximum strain energy per unit volume. Therefore, we need to divide the strain energy (U) by the volume of the body.

Resilience = U / Volume
= 500 J / (2 × 10^-4 m^3)
= 500 J / 0.0002 m^3
= 2,500,000 J/m^3
= 2,500 N-m/m^3
= 2,500 N-mmm^3

Since the volume is given as 2 × 10^5 mm^3, we can convert the units to N-mmm^3 by multiplying by 10^3.

Resilience = 2,500 N-mmm^3 * 10^3
= 2,500,000 N-mmm^3
= 100 N-mm (since 1 N-m = 1 N-mm)

Therefore, the resilience of the body is 100 N-mm, which corresponds to option A.