Mechanical Properties of Solids · NEET Preparation Physics

A wire of length L and radius r is rigidly fixed at one end. When a stretching force F is applied at the free end, the extension produced in the wire…

Practice question from Mechanical Properties of Solids (NEET Preparation Physics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-F035E9

A wire of length $L$ and radius $r$ is rigidly fixed at one end. When a stretching force $F$ is applied at the free end, the extension produced in the wire is $l$ . If another wire of the same material, length $2L$ and radius $2r$ is stretched with a force $2F$ , the extension produced will be:

A. $l$ Correct answer
B. $2l$
C. $l/2$
D. $4l$

Solution

Young's modulus is given by $Y = \frac{F/A}{\Delta L/L} = \frac{FL}{\pi r^2 l}$ . Therefore, extension $l = \frac{FL}{\pi r^2 Y}$ . For the second wire, $l' = \frac{(2F)(2L)}{\pi (2r)^2 Y} = \frac{4FL}{4 \pi r^2 Y} = \frac{FL}{\pi r^2 Y} = l$ .

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