Question

A large 75-kg lighting fixture can be hung from wires of identical size and shape made of aluminum, brass, or copper. The values of Young's modulus for these metals are 0.70 × 1011 Pa (aluminum), 0.91 × 1011 (brass), and 1.1 × 1011 (copper). Which wire would stretch the least distance?A. AluminumB. BrassC. CopperD. They will all stretch the same distance

Answer 1

Answer:

C. Copper

Explanation:

F = Force on string

$L_0$ = Intial length of string

A = Area of string

E = Young's modulus of material

Change in length is given by

$\Delta L=\frac{FL_0}{AE}$

It can be seen that the change in length is inversely proportional to the Young's modulus of the material.

Here

$E_a=0.7\times 10^{11}\ Pa$

$E_b=0.91\times 10^{11}\ Pa$

$E_c=1.1\times 10^{11}\ Pa$

$\\\Rightarrow E_c>E_b>E_a$

So, copper will stretch the least.