Which of the following statement is correct (A) Hooke's law is applicable only within elastic limit. (B) The adiabatic and isothermal elastic constants of a gas area equal. (C) Young's modulus is dimensionless. (D) Stress multiplied by strain is equal to stored energy.

Hooke's law states that the force needed to extend or compress a spring by some distance is proportional to that distance. This law holds true only within the elastic limit of the material. When the load exceeds the elastic limit, the material starts to undergo plastic deformation and Hooke's law does not apply anymore. Hence, this statement is true.

Adiabatic and isothermal elastic constants refer to the compressibility of a gas under adiabatic and isothermal conditions, respectively. The adiabatic elastic constant is greater than the isothermal elastic constant since the gas heats up during compression under adiabatic condition, making it harder to compress further. Thus, this statement is false.

Young's modulus (often denoted by Y or E) is a measure of the stiffness of an elastic material and is defined as the ratio of stress to strain. It has a unit of pressure, typically measured in pascals (Pa) or newtons per square meter (N/m^2). Since it has units, it is therefore not dimensionless. Hence, this statement is false.

In the context of materials under elastic deformation, the energy stored in the material is equal to the work done in deforming the material. The work done is given by the product of stress and strain. However, as stress and strain are not scalar quantities, their product does not give the energy directly. Hence, this statement is false. So, we have determined that: (A) Hooke's law is applicable only within elastic limit. - True (B) The adiabatic and isothermal elastic constants of a gas area equal. - False (C) Young's modulus is dimensionless. - False (D) Stress multiplied by strain is equal to stored energy. - False The correct statement among these is: Hooke's law is applicable only within elastic limit (Option A).