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

Explanation:

Given data,

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 =

Where,

F = applied force = mg = 100kg × 9.8ms-2 = 980 N

A = Area of one of the faces of the cube = L2 = 0.1×0.1 = 0.01m2

ΔL = vertical deflection of the cube.

Modifying the formula of Shear modulus,

ΔL =

Substituting all the values mentioned above, we get,

⇒ ΔL =

⇒ ΔL = 3.92 × 10-7m

Hence, the vertical deflection of this face of the cube is

3.92× 10-7 m.

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Answer 2

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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