In an experiment to determine the Young’s modulus, steel wires of five different lengths (1, 2, 3, 4 and 5 m) but of same cross section (2 mm2) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young’s modulus of given steel wires is x × 1011 Nm–2, then the value of x is ______.
Fig. Graph
In an experiment to determine the Young’s modulus, steel wires of five different lengths (1, 2, 3, 4 and 5 m) but of same cross section (2 mm2) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young’s modulus of given steel wires is x × 1011 Nm–2, then the value of x is ______.
Correct Answer: 2
Solution and Explanation
The correct answer is 2
\(Y = \frac{F×l}{A×Δl}\)
\(=\frac{1}{A}× \frac{Wire\ length}{\frac{Extension}{load}}\)
\(Y =\frac{1}{A}×(\frac{1}{0.25×10^{-5}})\)
\(Y = 10^{11}×2\)
⇒ x = 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:
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