Question

A rectangular block of a material $500mm$ long by $20mm$ wide by $300mm$ high has its lower face glued to a bench and a force of $200N$ is applied to the upper face and in line with it. The upper face moves $15$ mm relative to the lower face. If the shear modulus of the material is $n\times {10}^5$ Pa, n is:

• A. $4$
• B. $3$
• C. $6$
• D. $5$

Answer 1

The correct option is A $4$

Shearing stress$=\frac{\text{force}}{\text{area parallel to the force}}$
$=\frac{200N}{500mm\times 20mm}$

$=\frac{200}{(0.5\times 0.02)}N/m^2$

$=20000Pa$
Shearing strain $\varphi =\frac{15mm}{300mm}$
$=0.05$
Shearing modulus$=\frac{\text{Shearing stress}}{\text{Shearing strain}}$
$=\frac{20000}{0.05}$
$=400000Pa$
$=4\times {10}^{5}Pa$
$\Rightarrow n=4$