Question:
If a conical wire is stretched by two forces F applied, parallel to its length and In opposite direction. NoramI to end faces. The length of wire is L and its end radius are $r_1$ and $r_2$ Find out the extention produced (Given: Y=Young's modulus of wire)
If a conical wire is stretched by two forces F applied, parallel to its length and In opposite direction. NoramI to end faces. The length of wire is L and its end radius are $r_1$ and $r_2$ Find out the extention produced (Given: Y=Young's modulus of wire)
Updated On: Jul 6, 2022
- $\frac{FL}{\pi r^2_1 Y}$
- $\frac{FL}{\pi r_1 Y}$
- $\frac{FL}{\pi r_1r_2 Y}$
- $\frac{FL}{\pi r^2_1 }$
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The Correct Option is C
Solution and Explanation
$\Delta L = \frac{FL}{\gamma A} = \frac{FL}{\gamma \sqrt{A_1 A_2}} = \frac{FL}{\gamma \sqrt{\pi r_1^2 r_2^2}}$
$\Delta L = \frac{FL}{\gamma \, \pi \, r_1 r_2}$
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Concepts Used:
Mechanical Properties of Solids
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.