Two slabs with square cross section of different materials (1, 2) have equal sides l and thicknesses d₁ and d₂ such that d₂=2d₁ and ld₂. The lower edges of these slabs are fixed to the floor, and equal shearing forces are applied on the narrow faces. The angle of deformation is θ₂=2θ₁. If the shea…

Question

Two slabs with square cross section of different materials (1, 2) have equal sides l and thicknesses d₁ and d₂ such that d₂=2d₁ and l>d₂. The lower edges of these slabs are fixed to the floor, and equal shearing forces are applied on the narrow faces. The angle of deformation is θ₂=2θ₁. If the shear modulus of material 1 is 4×10⁹ N m⁻², then the shear modulus of material 2 is x×10⁹ N m⁻², where the value of x is .

Accepted Answer

1. Given: the same shearing force F on the narrow face of each slab, of area l d, and the same side l. Shear stress =F/(l d) and shear strain =θ, so G=F/(l d θ). With F and l common to both slabs, G∝1/(d θ). (G₂)/(G₁)=(d₁θ₁)/(d₂θ₂)=1/2×1/2=1/4. G₂=(4×10⁹)/4=1×10⁹ N m⁻², so x=1.

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