Question

A fixed volume of iron is drawn into a wire of length $l$. The extension produced in this wire by a constant force F is proportional to:
$A. {\text{ }}\dfrac{1}{{{l^2}}} \\\ B. {\text{ }}\dfrac{1}{l} \\\ C. {\text{ }}{l^2} \\\ D. {\text{ }}l \\\$

Answer 1

- Hint: Constant force can be defined as any force acting on an object to an unchanging rate. In other ways we can also say that the motion of an object on the surface of earth is to be pulled at the earth’s gravity which is an example of such a system with such a force.

Complete step-by-step answer:
Fixed volume of iron is used to draw a wire of length ‘L’. Extension ‘Y’ is produced in the wire by constant force ‘F’.
Formulas of volume and area are based on the lengths. therefore young’s modulus = stress/strain. given below the young’ modulus is applied where F is the applied force, L is the initial length, A is the square area.

$Y = \dfrac{{Fl}}{{A\Delta l}} \\\ \Delta l = \dfrac{{Fl}}{{YA}} \\\ V = A \times l \\\ A = \dfrac{V}{l} \\\ \Delta l = \dfrac{{F{l^2}}}{{YV}} \\\$
Therefore, option (C) is the right answer.

Volume refers to the space the amount of an object takes up. In other words, volume is a measure of the size of an object, just like width and height are ways to describe size. Volume is a measure of how much space an object takes up. Don’t get confused with mass and the volume both have different nature; mass and volume are both units used to measure objects. Mass is the amount of matter an object contains whereas the volume is how much space it takes up.

Note: The two terms used in volume and area are different in such a way; area gives the amount of space contained in a body of two dimensional realm whereas volume gives the amount of space contained in a body existing in a three dimension realm.