A square lead slab of side 50 cm and thickness 10 cm is subjected to a shearing force (on its narrow face) of $9 ? 10^4\, N$. The lower edge is riveted to the floor. How much will the upper edge be displaced? Shear modulus of lead $= 5.6 ? 10^9 \,N m^{-2}$
Updated On: Jul 6, 2022
$0.16\, mm$
$1.6\, cm$
$0.16\, cm$
$1.6\, mm$
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The Correct Option isA
Solution and Explanation
The lead slab is fixed and force is applied parallel to the narrow face as shown in the figure.
Area of the face parallel to which this force is applied is $A = 50\, cm ? 10 \,cm$$= 0.5 \,m ? 0.1\, m = 0.05\, m^2$
If $?L$ is the displacement of the upper edge of the slab due to tangential force $F$, then
$\eta=\frac{F / A}{\Delta L / L}$ or $\Delta L=\frac{\eta L}{YA}$
Substituting the given values, we get
$\Delta L=\frac{\left(9\times10^{4}\,N\right)\left(0.5\,m\right)}{5.6\times10^{9}\,N\,m^{-2}\times0.05\,m^{2}}$$=1.6\times10^{-4}\,m=0.16\,mm$
Mechanical properties of solids intricate the characteristics such as the resistance to deformation and their strength. Strength is the ability of an object to resist the applied stress, to what extent can it bear the stress.
Therefore, some of the mechanical properties of solids involve:
Elasticity: When an object is stretched, it changes its shape and when we leave, it retrieves its shape. Or we can say it is the property of retrieving the original shape once the external force is removed. For example Spring
Plasticity: When an object changes its shape and never attains its original shape even when an external force is removed. It is the permanent deformation property. For example Plastic materials.
Ductility: When an object is been pulled in thin sheets, wires or plates, it will be assumed that it has ductile properties. It is the property of drawing into thin wires/sheets/plates. For example Gold or Silver
Strength: The ability to hold out applied stress without failure. Many types of objects have higher strength than others.
