Explanation:
Strain energy is the energy stored in a body due to deformation. It is the work done in deforming the material and is stored as potential energy.

The formula for strain energy stored in a solid is given by:

U = 0.5 x σ x ε x V

where U is the strain energy stored in the solid, σ is the stress applied, ε is the strain produced, and V is the volume of the solid.

In other words, the strain energy stored in a solid is directly proportional to the stress applied, the strain produced, and the volume of the solid.

Option D is the correct answer as it includes all the variables mentioned in the formula.

Let's break down the formula and understand each variable:

0.5: This is a constant factor that arises due to the integration of the stress-strain curve.

σ: Stress is the force applied per unit area. It is the external force that causes the deformation in the material.

ε: Strain is the ratio of change in length to the original length of the material. It is the measure of deformation produced in the material.

V: Volume is the amount of space occupied by the material. It is the three-dimensional space that the material occupies.

Therefore, the formula for strain energy stored in a solid depends on the stress applied, strain produced, and the volume of the solid.

Conclusion:
The correct formula for strain energy stored in a solid is U = 0.5 x σ x ε x V. It is directly proportional to the stress applied, strain produced, and the volume of the solid. Option D is the correct answer as it includes all the variables mentioned in the formula.