Q6  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?

Answers (1)
S Sayak

Edge of the aluminium cube, l = 10 cm = 0.1 m

Area of a face of the Aluminium cube, A = l2 = 0.01 m2

Tangential Force is F 

\\F=100\times 9.8\\ F=980\ N

Tangential Stress is F/A

\\\frac{F}{A}=\frac{980}{0.01}\\ \frac{F}{A}=98000N

Shear modulus of aluminium \eta =2.5\times 10^{10}Nm^{-2}

\\Tangential\ Strain=\frac{\frac{F}{A}}{\eta }\\ =\frac{98000}{2.5\times 10^{10}}\\ =3.92\times 10^{-6}

Let the Vertical deflection be \Delta l

\\\Delta l=Tangential\ Stress\times Side \\\Delta l=3.92\times 10^{-6}\times 0.1\\ \Delta l=3.92\times 10^{-7}m