Question

(C) LAUV-UL
If a bar is made of copper whose coefficient of linear
expansion is one and a half times that of iron, the ratio of
force developed in the copper bar to the iron bar of identical
lengths and cross-sections, when heated through the same
temperature range (Young's modulus of copper may be taken
to be equal to that of iron) is
(a) 3/2 (6) 2/3 (c) 9/4 (d) 4/9​

Answer 1

Answer:

Here force developed is given as,

F

=

Y

α

t

A

F=YαtA

where

Y

t

A

YtA is constant for both copper and iron rod.

now

F

∝

α

F∝α

and it is given that coefficient of thermal expansion

α

c

o

p

p

e

r

=

3

2

α

i

r

o

n

αcopper=32αiron

hence

F

c

F

i

=

α

c

α

i

=

3

2

FcFi=αcαi=32