Question

A dress made of cloth will hang nicely, conforming to the shape of the body beneath, because cloth both

• A. a large Young's modulus and a low bulk modulus
• B. a low shear modulus and a low Young's modulus
• C. a large Young's modulus and a low shear modulus
• D. a low bulk modulus and a high shear modulus

Answer 1

Answer: (B)

a low shear modulus and a low Young's modulus

Answer 2

A dress made of cloth hangs nicely and conforms to the body's shape because cloth is flexible. Flexibility in this context means it can easily bend, fold, and stretch slightly under stress.

• Low Shear Modulus ($\eta$): The ability to bend and fold easily is primarily related to the shear modulus. A low shear modulus means the material offers little resistance to shearing forces, allowing its layers to slide past each other, which is essential for forming pleats and conforming to curves.
• Low Young's Modulus (Y): Young's modulus relates to the material's resistance to stretching or compression. A low Young's modulus means the cloth can stretch slightly under its own weight (due to gravity) or when conforming to the body's contours, which contributes to a smooth drape.

A high Young's modulus or a high shear modulus would make the cloth stiff and less able to drape. Bulk modulus is less relevant for draping, which is primarily a surface and bending phenomenon. Therefore, a cloth with a low shear modulus and a low Young's modulus will hang nicely.