# two rods of lengths l1 and l2 are made of materials whose co-efficient of linear expansion are a1 an a2. ​If the increase in length be same at all temperatures then(i) l1/l2=a1/a2(ii) l1/l2=a2/a1(iii)  l1 + a1 = l2 + a2 (iv) l1/a12=l2/a22

arun
123 Points
7 years ago
answer is (ii). it is given that change in length is same for both rods. now,
${\color{Red} \Delta l=laT}$
here, red coloured l, a represents the l1 and a1
and green coloured represents l2 and a2
${\color{Green} \Delta l=laT}$
and it is given${\color{Green} \Delta l}={\color{Red} \Delta l}$
$\Rightarrow {\color{Red} lat}={\color{Green} lat}$
also${\color{Red} t}={\color{Green}t}$
$\Rightarrow \frac{{\color{Red} l}}{{\color{Green} l}}=\frac{{\color{Green} a}}{{\color{Red} a}}$
so l1/l2=a2/a1