Final answer:
The statement is false as a material with a large Young's modulus will deform less, not more, compared to a material with a small Young's modulus under the same stress.
Step-by-step explanation:
The statement that a material with a large Young's modulus (E) will extend more than a material with a small E at a given stress is false. In fact, Young's modulus (E) is a measure of a material's tensile stiffness, and indicates how much it will deform under a certain stress. A high elastic modulus means the material is less pliable and deforms less under the same stress compared to a material with a low elastic modulus. This relationship between stress and strain (deformation) is captured in what's known as Hooke's Law and represented in engineering and construction data tables for various materials.
Consider two materials, rubber with a low E and steel with a high E. Under the same tensile stress, rubber will experience a larger strain or deformation compared to steel because it has a lower Young's modulus. Therefore, a material with a large Young's modulus has a higher resistance to deformation and thus deforms less under the same stress compared to materials with low Young's moduli.