Read the following two statements below carefully and state, with reasons, if it is true or false. (a) The Young's modulus of rubber is greater than that of steel; (b) The stretching of a coil is determined by its shear modulus.
False - The Young's modulus of rubber is NOT greater than that of steel. According to the context, metals have larger values of Young's modulus than alloys and elastomers. Steel is a metal while rubber is an elastomer. A material with large Young's modulus requires a large force to produce small changes in its length. Steel is more elastic than rubber because it stretches less for a given load.
True - The stretching of a coil is determined by its shear modulus. When a coil (spring) is stretched, the wire of the coil undergoes a twisting or shearing deformation rather than simple elongation. As per the context, shear modulus (modulus of rigidity) relates shear stress to shear strain for solids, and this is the relevant elastic constant for the deformation of a coil under tension.
Explanation
For statement (a): The context clearly states that 'Metals have larger values of Young's modulus than alloys and elastomers.' Steel is a metal and rubber is an elastomer, so steel has greater Young's modulus. The context also clarifies that 'material which stretches to a lesser extent for a given load is considered to be more elastic' - steel stretches less than rubber for the same load. For statement (b): When a coil spring is stretched, each turn of the coil experiences a twisting force that causes shear deformation in the wire. The shear modulus describes the relationship between shear stress and shear strain, making it the appropriate elastic constant for coil stretching.