Question

Aluminum Rod#1 has a length L and a diameter d. Aluminum Rod#2 has a length 2L and a diameter 2d. If Rod#1 is under tension T and Rod#2 is under tension 2T, how do the changes in length of the two rods compare?
A) Rod #2 has quadruple the change in length that Rod #1 has.
B) Rod #2 has double the change in length that Rod #1 has.
C) Rod #1 has double the change in length that Rod #2 has.
D) They are the same.
E) Rod #1 has quadruple the change in length that Rod #2 has.

Answer 1

Answer:D

Explanation:

For Rod 1

length,diameter and Tension is L, d and T

for Rod 2 length,diameter and Tension is 2L, 2d and 2T

Change in Length is given by

$\Delta =\frac{PL}{AE}$

where P=load

L=length

A=area of cross-section

E=young's Modulus

$\Delta _1=\frac{TL}{\frac{\pi d^2}{4}E}$

since both are aluminium rod therefore E is common

$\Delta _2=\frac{2T\cdot 2L}{\frac{\pi (2d)^2}{4}E}$

$\Delta _2=\frac{TL}{\frac{\pi d^2}{4}E}=\Delta _1$

Thus extension in both the rods are same