Question

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 1

$\huge \mathfrak{Answer}$

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 × 109 Pa

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

Where,

F = Applied force = mg = 100 × 9.8 = 980 N

A = Area of one of the faces of the cube = 0.1 × 0.1 = 0.01 m2

ΔL = Vertical deflection of the cube

∴ ΔL = FL / Aη

= 980 × 0.1 / [ 10-2 × (25 × 109) ]

= 3.92 × 10–7 m

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

Answer 2

putting the values in the above formula u get the answer.