Question

A cube of sponge rubber with edge length 5 cm has a force of 2 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 mm, find the shear modulus for the sponge rubber.

• A. $S=7\times {10}^{4}N{m}^{-2}$
• B. $S=6\times {10}^{4}N{m}^{-2}$
• C. $S=4\times {10}^{4}N{m}^{-2}$
• D. $S=5\times {10}^{4}N{m}^{-2}$

Answer 1

The correct option is C $S=4\times {10}^{4}N{m}^{-2}$

$\eta =\frac{F}{A}\times \frac{l}{n}$

$=\frac{2\times {\left(100\right)}^2}{5\times 5}\times \frac{5\times 1000}{100\times 1}$

$=\frac{2\times 2\times {10}^5}{5\times 2}$

$S=4\times {10}^{4}N{m}^{-2}$