Question

A tangential force of $4200N$ is applied on a surface of area $6\times {10}^{-6}{m}^2$ which is $0.2m$ from a fixed face. The force produces a shift of 14mm of upper surface with respect to bottom. The rigidity modulus of material is :

• A. ${10}^{10}N/m^2$
• B. ${10}^{8}N/m^2$
• C. ${10}^{6}N/m^2$
• D. ${10}^{12}N/m^2$

Answer 1

The correct option is A ${10}^{10}N/m^2$

$Stress=M\left(Strain\right),\text{here}M\text{is rigidity modulus}$
$Stress=\frac{F}{A}$
$Stress=\frac{4200}{6\times {10}^{-6}}$
$Stress=7\times {10}^8$

$Strain=\frac{l}{L}$
$Strain=\frac{14\times {10}^{-3}}{0.2}$
$Strain=7\times {10}^{-2}$
$M=\frac{7\times {10}^8}{7\times {10}^{-2}}$
$M={10}^{10}N/m^2$
where strain is unitless.