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Which apparatus are used to measure $Y$ of a wire and shear modulus of the wire?(A) Searle’s Apparatus, Ewing extensometer(B) Searle’s Apparatus, Maxwell needle method(C) Searle’s Apparatus, Torsion pendulum(D) Kundt’s Apparatus, Searle’s Apparatus

Last updated date: 20th Jun 2024
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Hint:Here, you are given various apparatus and are asked to find the correct apparatus which is used to find the $Y$ of a wire and shear modulus of a wire. Here, $Y$ is the Young’s modulus. In order to answer this question, you need to consider each apparatus separately and then determine what quantities are or can be derived using the given apparatus.

Consider a wire which is being stretched by a force $F$, let the length of the wire be $l$, elongation in the wire be $\Delta l$ and cross section be $A$. The Young’s modulus is given as $Y = \dfrac{{Fl}}{{A\Delta l}}$ , the ratio of longitudinal stress and longitudinal strain.Whereas, the shear modulus is the ratio of shear stress and shear strain.
Torsion pendulum consists of a wire which is attached to a rigid support and the other end is connected to a heavy disc. This method also uses the time period of oscillation of the disc in order to determine the Shear modulus of the wire.Kundt’s apparatus is an acoustical apparatus used to determine the speed of sound in air or gases. Therefore, Searle’s Apparatus, Maxwell needle method and Torsion pendulum are used to measure $Y$ and shear modulus of the wire.