Question

The edge of an aluminium cube is $10cm$ long. One face of the cube is firmly fixed to a vertical wall. A mass of $100kg$ is then attached to the opposite face of the cube. The shear modulus of aluminium is $25GPa$ . What is the vertical deflection of this face?

• A. $3.92\times 10^{-7}m$
• B. $5.98\times 10^{-7}m$
• C. $2.72\times 10^{-7}m$
• D. $4.82\times 10^{-7}m$

Answer 1

Answer: (A)

Given, side of a cube (l) = 10 cm = 0.1 m
​Area its each face (A) = l² = (0.1)² = 0.01 m²
Load (m) = 100 kg
Tangential force acting on one face of the cube,
​F = mg = 100 × 9.8 = 980 N
$\text{Shear stress acting on this face}=\frac{\text{F}}{\text{A}}$
$=\frac{\text{980}}{\text{0.01}}{\text{N/m}}^2$
= 9.8 × 10⁴ N/m²
Shear modulus of aluminium (η)) = 25 GPa
= 25 × 10⁹ N/m²
$\text{Shear modulus}\left(\eta \right)=\frac{\text{Shearing stress}}{\text{Shearing strain}}$
$\text{or shearing strain}\left(\frac{\text{Δ}\text{y}}{\text{L}}\right)=\frac{\text{Shearing stress}}{\text{Shear modulus}}$
$\text{or}\text{Δ}\text{y}=\frac{\text{Shearing stress}}{\text{Shear modulus}}\times \text{L}$
$=\frac{\text{9.8}\times {\text{10}}^4}{\text{25}\times {\text{10}}^9}\times \text{0.1}$
= 0.392 × 10^-5 m
= 3.92 × 10^-7 m