The edge of an aluminium cube is 10 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 100 kg is then attached to the opposite face of the cube. The shear modulus of aluminium is 25 GPa . What is the vertical deflection of this face?

Step-by-step solution

Given, side of a cube (l) = 10 cm = 0.1 m ​Area its each face (A) = l 2 = (0.1) 2 = 0.01 m 2 Load (m) = 100 kg Tangential force acting on one face of the cube, ​F = mg = 100 × 9.8 = 980 N Shear stress acting on this face = F A = 980 0.01 N/m 2 = 9.8 × 10 4 N/m 2 Shear modulus of aluminium (η)) = 25 GPa = 25 × 10 9 N/m 2 Shear modulus η = Shearing stress Shearing strain or shearing strain Δ y L = Shearing stress Shear modulus or Δ y = Shearing stress Shear modulus × L = 9.8 × 10 4 25 × 10 9 × 0.1 = 0.392 × 10 -5 m =