Question

A steel plate of upper face area $2{\text{cm}}^2$ and thickness $6\text{cm}$ is fixed rigidly at the lower surface. A tangential force $F=20\text{kN}$ is applied on the upper surface as shown in the figure. The lateral displacement $x$ of upper surface w.r.t the lower surface is (Take modulus of rigidity for steel is $8\times {10}^{11}{\text{N/m}}^2$).

• A. $7.5\times {10}^{-6}\text{m}$
• B. $30\times {10}^{-6}\text{m}$
• C. $15\times {10}^{-6}\text{m}$
• D. $3.5\times {10}^{-6}\text{m}$

Answer 1

The correct option is A $7.5\times {10}^{-6}\text{m}$

We know, modulus of rigidity $\left(G\right)=\frac{FL}{Ax}.......\left(1\right)$
where $F=$ Tangential force
$A=$ Face area
$x=$ Lateral displacement
Given,
$F=20\times {10}^3\text{N}$
$L=6\text{cm}=0.06\text{m}$
$A=2\times {10}^{-4}{\text{m}}^2$
$G=8\times {10}^{11}{\text{N/m}}^2$
Substituting the values in equation $\left(1\right)$, we get
$8\times {10}^{11}=\frac{20\times {10}^3\times 0.06}{2\times {10}^{-4}\times x}$

$\Rightarrow x=7.5\times {10}^{-6}\text{m}$