What is the ratio of the shear strain for the larger object to that of the smaller object?

Question

Shear forces are applied to a rectangular solid. The same forces are applied to another rectangular solid of the same material, but with three times each edge length. In each case the forces are small enough that Hooke's law is obeyed.

Answer 1

Elastic modulus = Stress/Strain = (Force/Area)/DeltaX/h

since all we really care about is ratio between the strain

Strain = Stress/ElasticModulus

The modulus is a constant as is the force in this question, therefore the only affecting variable is Area, which is L x W or L^2 for a square.

Ratio = L^2/(3L)^2