# Question 2b1f4

Feb 10, 2017

$2.0 \times {10}^{3} \text{ Pa}$

#### Explanation:

As shown in the figure bottom face of the sample is held rigidly bound and a shearing/tangential force $F$ is applied on upper face of area $A$. The modulus of rigidity $G$ is defined as the ratio of shear stress to the shear strain.

Shear stress$= \frac{F}{A}$ and
shear strain $= \tan \theta = \frac{\Delta x}{l}$
$\Delta x$ is the transverse displacement of the area on which force is acting and $l$ is the initial length of the side.

G -= "Shear stress"/"Shear strain"= (F / A)/ ((Δ x) / l)
=>G= (F l)/( A Δ x)" Pa"#

Inserting given values in SI units we get

$G = 10 \times \frac{\frac{10}{100}}{\frac{0.05}{100}}$
$\implies G = 10 \times \frac{10}{0.05}$
$\implies G = 2.0 \times {10}^{3} \text{ Pa}$