WBJEE 2024 Physics & Chemistry Paper

The elastic potential energy stored in a strained body can be derived from the relationship between stress, strain, and the deformation energy per unit volume. This relationship is often represented using the formula for the elastic potential energy density in a material. The correct option is:
Option D: ‌

1

2

× stress × strain × volume
Explanation:
Elastic potential energy is the energy stored in an object when it is deformed but not permanently. When a material follows Hooke's Law, the stress (force per unit area) and strain (deformation per unit length) are linearly related. The formula for elastic potential energy U in a body is given by:
U=‌

1

2

×‌ stress ‌×‌ strain ‌×‌ volume ‌
Where:
- Stress is the internal force per unit area within the material.
Strain is the relative deformation, i.e., the change in length divided by the original length.
Volume is the measure of the space occupied by the body where the deformation occurs.
The factor ‌

1

2

comes from the integration of the linear stress-strain relationship, considering that stress increases linearly with strain from 0 to its maximum value. Thus, the correct representation of the elastic potential energy is given by Option D.