Explanation:
To understand why the strain energy absorbed by the shank doubles when its length is doubled, let's first define what strain energy is and how it is related to the length of a structure.

Strain Energy:
Strain energy is the energy stored in a material when it is deformed under load. It is a measure of the elastic potential energy stored in a material due to the work done to deform it. In other words, it is the energy required to deform a material and is released when the material returns to its original shape.

Relationship between Strain Energy and Length:
The strain energy stored in a structure is directly proportional to its length. This relationship is derived from the formula for strain energy, which is given by:

Strain Energy = (1/2) * Stress * Strain * Volume

Here, the volume of the structure is directly proportional to its length. Therefore, when the length of the shank is doubled, the volume also doubles. As a result, the strain energy stored in the shank also doubles.

Answer:
Based on the above explanation, it can be concluded that when the length of the shank is doubled, the strain energy absorbed by the shank also doubles. Therefore, option 'A' is the correct answer.

Note:
It is important to note that this relationship assumes that the material properties and the applied load remain constant. In practical scenarios, other factors such as the material's behavior under load, the type and magnitude of the applied load, and other geometric considerations may also affect the strain energy absorbed by a structure.