Question

: Two wires with equal lengths are made of pure copper. The diameter of wire A is twice the diameter of wire B. When 6kg masses are hung on the wires, wire B stretches more than wire A. You make careful measurements and compute young’s modulus for both wires. What do you find? (a) $Y_A>Y_B$, b) $Y_A=Y_B$c) $Y_A<Y_B$

Short answer

(b) $Y_A=Y_B$

Step-by-step solution

Identification of the given data

The given data can be listed below as-

• The mass of the objects are of .

Significance of the Young’s modulus

Young’s modulus is the property of the material and depends on temperature and pressure. It depends on the nature of the material and it independent of the shape and width.

The equation of the Young’s modulus gives the relation between the Young’s modulus of both the wires.

Determination of the Young’s modulus for the wires

The Young’s modulus of a wire made of a material is given by,

$Y=\frac{Fl}{A∆l}$

Where,$∆l$ = change in length, F= force applied load (load), L = original length and A= Cross sectional area

Here, the diameter of the wire A is twice the diameter of the wire B but the stretch happens more in wire B. Hence, the ratio of the stress and the strain for the wires are equal as it is independent on the size and the shape of the material. As the ratio of the stress and the strain for both the wires are equal, Hence, the Young’s modulus for both wires will be equal.

Thus, b) is the correct option.