Question:
Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3A$. If the length of the first wire is increased by $\Delta l$ on applying a force $F$, how much force is needed to stretch the second wire by the same amount ?
Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3A$. If the length of the first wire is increased by $\Delta l$ on applying a force $F$, how much force is needed to stretch the second wire by the same amount ?
Updated On: Jul 18, 2024
- F
- 9 F
- 4 F
- 6 F
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The Correct Option is B
Solution and Explanation
For wire 1,
$\Delta I = \left(\frac{F}{AY}\right)3I $ ......(i)
For wire 2,
$\frac{F'}{3A} = Y \frac{\Delta I}{I}$
$ \Rightarrow \Delta I = \left(\frac{F'}{3AY}\right)I$ ....(iii)
From equation (i) & (ii),
$ \Delta I = \left(\frac{F}{AY}\right) 3I = \left(\frac{F'}{3AY}\right)I$
$ \Rightarrow F' = 9F $
$\Delta I = \left(\frac{F}{AY}\right)3I $ ......(i)
For wire 2,
$\frac{F'}{3A} = Y \frac{\Delta I}{I}$
$ \Rightarrow \Delta I = \left(\frac{F'}{3AY}\right)I$ ....(iii)
From equation (i) & (ii),
$ \Delta I = \left(\frac{F}{AY}\right) 3I = \left(\frac{F'}{3AY}\right)I$
$ \Rightarrow F' = 9F $
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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.