Question

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

Answer 1

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.

Complete answer:
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.

Searle’s apparatus consists of two wires which are attached to rigid supports. The other ends of both the wires are connected to a horizontal bar. A spirit level is mounted on the horizontal bar. If the weight on any of the wire is increased, it elongates and the spirit level is tilted. This is a brief description of Searle’s method. Searle’s apparatus is used to measure the Young’s modulus of a material as it involves the elongation of wire and that is what we want in order to determine the Young’s modulus.

Ewing extensometer is a device which is used to calculate the change in lengths. It is not useful to find the shear modulus.Maxwell needle method consists of a maxwell needle, a wire, two hollow cylinders and two solid cylinders. It calculates the time periods of oscillation of two set-up. In one case, the hollow cylinders are kept inside and the solid cylinders are kept outside and in the other case, solid cylinders are kept inside and hollow ones are kept outside. This is a brief description of Maxwell needle method. The method is used to determine the Shear modulus of a material.

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.

Hence, option B and C are correct.

Note:we have discussed in brief the apparatus of various experiments and you need to keep in mind which experiment is used to determine what quantity. Searle’s apparatus is used to determine the Young’s modulus, Maxwell needle method and torsion pendulum are used to determine the Shear modulus, Ewing extensometer is used to determine the change in length and Kundt’s tube is used to determine the speed of sound.