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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?

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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

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