Question

A copper rod of 88 cm and an aluminium rod of
unknown length have their increase in length
independent of increase in temperature. The length
of aluminium rod is : (ac, = 1.7x 10-5 K-1 and
a =2.2x10-50-1)
(1)
113 am
113.9 cm
(2)
88 cm
68 cm
6.8 cm
​

Answer 1

according to question,

a copper rod and aluminium rod in such a way that increase their lengths do not depend on increase in temperature.

it means,

change in length of copper = change in length of aluminium

or, $l_c\alpha_c=l_a\alpha_a$

it is given that ,

length of copper rod, $l_c$ = 88cm.

coefficient of linear expansion of copper = 1.7 × 10^-5 /K

and coefficient of linear expansion of aluminium = 2.2 × 10^-5 /K

now, 88cm × 1.7 × 10^-5 = l × 2.2 × 10^-5

or, l = 68cm

hence, length of aluminium rod is 68cm