Question

A cube of sponge rubber with edge length $5\text{cm}$ has a force of $2\text{N}$ applied horizontally to the top face (parallel to an edge) while the bottom face is held fixed. If the top face is displaced horizontally through a distance of $1\text{mm}$, find the shear modulus for the sponge rubber.

• A. $4\times {10}^4{\text{N/m}}^2$
• B. $8\times {10}^4{\text{N/m}}^2$
• C. $24\times {10}^4{\text{N/m}}^2$
• D. $32\times {10}^4{\text{N/m}}^2$

Answer 1

The correct option is A $4\times {10}^4{\text{N/m}}^2$

Shear Modulus is given by

$G=\frac{\text{shear Sress}}{\text{shear Strain}}$

Shear strain $=\varphi \approx \tan \varphi =\frac{{10}^{-3}}{5\times {10}^{-2}}$ $=0.02$

Shear stress$=\frac{F}{A}=\frac{2}{25\times {10}^{-4}}=800{\text{N/m}}^2$

$\therefore$ Shear Modulus, $G=\frac{800}{0.02}=4\times {10}^4{\text{N/m}}^2$

Hence, option $\left(\text{A}\right)$ is correct.