Question

A steel plate of face area ${4cm}^{-2}$ and thickness 0.5 cm is fixed rigidly at the lower surface. A tangential force of 10 N is a pplied on the upper surface. Find the lateral displacement of the upper surface with respect to the lower surface. Rigidity modulus of steel. $(8.4\times {10}^{10}{Nm}^{-1})$

Answer 1

Given Data:

Area of steel plate, $4c{m}^{-2}=4\times {10}^{-4}{m}^{-2}$

Thickness $=0.5cm=5\times {10}^{-3}m$

$\text{F = 10 N}$

Rigidity modulus of stee, $m=$ $(8.4\times {10}^{10}{Nm}^{-1})$

Angular Displacement, $m=\frac{F}{A\theta }⟹8.4\times {10}^{10}=\frac{10}{4\times {10}^{-4}\theta }=0.297\times {10}^{-6}$

Lateral displacement

= $\theta .d$ $⟹0.5\times {10}^{-2}\times 0.297\times {10}^{-6}=1.5\times {10}^{-9}m$