Question

The ends 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

Edge of the aluminium cube, L = 10 cm = 0.1 m
The mass attached to the cube, m = 100 kg
Shear modulus (?) of aluminium = 25 GPa = 25 � 109 Pa
Shear modulus, ?
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
?L = Vertical deflection of the cube

= 3.92 � 10�7 m
The vertical deflection of this face of the cube is 3.92 �10�7 m.

Answer 2

Hii dear,

◆ Answer-
Vertical deflection = 3.92×10^-7 m

◆ Explanation-
# Given-
s = 10 cm = 0.1 m
m = 100 kg
η = 25 GPa = 25×10^9 Pa

# Solution
Shear modulus of aluminum is calculated by-
η = Shear stress / Shear strain
η = (F/A) / (s/Δs)
η = (mgs^2) / (s/∆s)
∆s = mg / sη
∆s = 100×9.8 / 0.1×25×10^9
∆s = 3.92×10^-7 m

Hence, the vertical deflection of this face of the cube is 3.92×10^–7 m.

Hope this is helpful...