Specific tensile modulus is defined as the elastic modulus of a material divided by its density.

• A. The density divided by the elastic modulus.
• B. The tensile strength divided by density.
• C. The energy absorbed before fracture.
• D. The elastic modulus divided by density.

Answer: (D)

Specific modulus measures stiffness per unit weight. It captures how stiff a material is for a given mass, which is crucial when weight is a critical constraint in design. It is defined as the elastic modulus divided by the density (E/ρ). Here, E tells you how resistant the material is to elastic deformation, while ρ tells you how much mass occupies a volume. Their ratio, E/ρ, tells you how much stiffness you get per unit mass, and a higher value means you can achieve greater stiffness without adding much weight. An added intuition: the square root of E/ρ corresponds to the speed of sound in the material, linking this ratio to how quickly stress waves propagate and reinforcing why stiffness per weight matters physically.

Dividing density by modulus would give the inverse of this quantity, not the defined specific modulus. The energy absorbed before fracture relates to toughness, a different property. And dividing tensile strength by density would give a specific strength, another metric focused on strength rather than stiffness. So the ratio of elastic modulus to density best represents stiffness per weight, which is exactly what specific modulus measures.