ii A 100 MPa force is applied to the surface of a material (surface area, 1m^2 ) that exerts a shear across the material. The sample has a thickness of 10 cm and causes the surface to be displaced by 0.1 cm. What is the shear modulus of the material? (3 marks)

To find the shear modulus of the material, we can use the formula:<br /><br />Shear Modulus (G) = (Shear Stress) / (Shear Strain)<br /><br />Given information:<br />- Applied force (F) = 100 MPa = 100,000,000 Pa<br />- Surface area (A) = 1 m²<br />- Thickness (h) = 10 cm = 0.1 m<br />- Displacement (δ) = 0.1 cm = 0.001 m<br /><br />First, let's calculate the shear stress (τ):<br /><br />τ = F / A<br />τ = 100,000,000 Pa / 1 m²<br />τ = 100,000,000 Pa<br /><br />Next, let's calculate the shear strain (γ):<br /><br />γ = δ / h<br />γ = 0.001 m / 0.1 m<br />γ = 0.01<br /><br />Now, we can calculate the shear modulus (G):<br /><br />G = τ / γ<br />G = 100,000,000 Pa / 0.01<br />G = 10,000,000,000 Pa<br /><br />Therefore, the shear modulus of the material is 10,000,000,000 Pa.