Two rods, one of aluminium and the other made of steel ,having initial length l1 + l2. are connected together to form a single rod of length l1+l2. The coefficients of linear expansion for aluminium and steel are αa and αs respectively. if the lenghth of each rod increases by the same amount when their temperature are raised by t°C, then find the ratio (l1/l1+l2)

Question

Two rods, one of aluminium and the other made of steel ,having initial length l1 + l2. are connected together to form a single rod of length l1+l2. The coefficients of linear expansion for aluminium and steel are αa and αs respectively. if the lenghth of each rod increases by the same amount when their temperature are raised by t°C, then find the ratio (l1/l1+l2) (A) (αs /αa) (B) (αa /αs) (C) (αs /(αa+αs)) (D) (αa /(αa+αs)

Tardigrade Admin · Accepted Answer

Given Δ l1 =Δ l2 or l1αa t =l2 αs l ∴ (l1/l2)=(αs/αa) or (l1/l1 +l2) =(αs/αa +αs)

$\frac{α _{s}}{α _{a}}$

$\frac{α _{a}}{α _{s}}$

$\frac{α _{s}}{( α _{a} + α _{s} )}$

$\frac{α _{a}}{( α _{a} + α _{s}}$

Given $Δ l_{1} = Δ l_{2}$ or $l_{1} α_{a} t = l_{2} α_{s} l$
$∴ \frac{l _{1}}{l _{2}} = \frac{α _{s}}{α _{a}}$ or $\frac{l _{1}}{l _{1} + l _{2}} = \frac{α _{s}}{α _{a} + α _{s}}$

αa​αs​​

αs​αa​​

(αa​+αs​)αs​​

(αa​+αs​αa​​

Given Δl1​=Δl2​ or l1​αa​t=l2​αs​l ∴l2​l1​​=αa​αs​​ or l1​+l2​l1​​=αa​+αs​αs​​

$\frac{α _{s}}{α _{a}}$

$\frac{α _{a}}{α _{s}}$

$\frac{α _{s}}{( α _{a} + α _{s} )}$

$\frac{α _{a}}{( α _{a} + α _{s}}$

Given $Δ l_{1} = Δ l_{2}$ or $l_{1} α_{a} t = l_{2} α_{s} l$
$∴ \frac{l _{1}}{l _{2}} = \frac{α _{s}}{α _{a}}$ or $\frac{l _{1}}{l _{1} + l _{2}} = \frac{α _{s}}{α _{a} + α _{s}}$