Question

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.

Answer 1

(a) “The Young’s modulus of rubber is greater than that of steel.”

Statement: False.

• Young’s modulus measures stiffness: the larger the modulus, the smaller the strain produced by a given stress.
• Rubber undergoes large elongations even under small forces, i.e. it is much more easily stretched → its Young’s modulus is much smaller than that of steel.
• Steel is far stiffer (very small strain for a given stress), so steel has a much higher Young’s modulus than rubber.

(b) “The stretching of a coil is determined by its shear modulus.”

Statement: True (for a helical coil/spring).

• A helical spring (coil) made of wire does not mainly extend by simple axial stretching of the material.
• When a helical coil is stretched, the wire forming the coil is twisted; the deformation is predominantly shear/torsional in the material of the wire.
• Therefore, the extension of a helical coil is governed mainly by the shear modulus (modulus of rigidity) of the material, not directly by its Young’s modulus.