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? question 9.6 machenical properties of solid

Answer 1

Shear ' s modulus (η) of aluminium = 25 GPa 

= 25 x 10⁹ Pa 

Shear's Modulus , η = shear stress / shear strain 

⇒ (F/A) /(L/ΔL) 

⇒ ΔL = FL/Aη

⇒ 9.8 x 0.1 / 10⁻² x (25 x 10⁹) 

= 3.92 x 10⁻⁷ m 

Answer 2

given,
side of a cube (l) = 10cm = 0.1 m
area of its face = (side  length)²
                       = (0.1)² = 0.01 m²
normal force acting each face of cube = mg = 100×9.8 = 980 N
now,
 shear modulus = shearing stress acting on this  face/shearing strain acting on this face 

25GPa ={ 980 N/0.01 m²}/strain
strain = 98000/25×10⁹
   ΔL/L  =3.92 × 10⁻6 
ΔL = 3.92 × 10⁻⁶× 0.1 = 3.92 ×10⁻⁷ m
hence deflection of this face =3.92 ×10⁻⁷ m