### Q.6:- 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?

**Answer:-**Edge of the aluminium cube, *L* = 10 cm = 0.1 m

The mass attached to the cube, *m* = 100 kg

Shear modulus (η) of aluminium = 25 GPa = 25 × 10^{9} Pa

Shear modulus, η = Shear stress / Shear strain = (F/A) / (*L*/Δ*L)*

Where,

*F* = Applied force = *m*g = 100 × 9.8 = 980 N

*A* = Area of one of the faces of the cube = 0.1 × 0.1 = 0.01 m^{2}

Δ*L* = Vertical deflection of the cube

∴ Δ*L* = *FL* / *A*η

= 980 × 0.1 / [ 10^{-2} × (25 × 10^{9}) ]

= 3.92 × 10^{–7} m

The vertical deflection of this face of the cube is 3.92 ×10^{–7} m.