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Properties of Matter question

2016 · Q152
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Properties of Matter question

2016 · Q152

NEETPhysicsProperties of MatterMCQ+4 / −1
Coefficient of linear expansion of brass and steel rods are α\alphaα1 and α\alphaα2. Lengths of brass and steel rods are lll1 and lll2 respectively. If (lll1 −-− lll2) is maintained same at all temperatures, which one of the following relations holds good?
  1. A
    α\alphaα1lll2 = α\alphaα2 2lll1
  2. B
    α\alphaα1lll1 = α\alphaα2l2
  3. C
    α\alphaα1lll2 = α\alphaα2lll1
  4. D
    α\alphaα1lll22 = α\alphaα2lll12
View written solutionFree

Correct answer: B

From question, (l2−l1)\left( {{l_2} - {l_1}} \right)(l2​−l1​) is maintained same at all temperatures hence change in length for both rods should be same

i.e., Δl1=Δl2\Delta {l_1} = \Delta {l_2}Δl1​=Δl2​

As we know, coefficient of linear expansion,

α=Δll0ΔT\alpha = {{\Delta l} \over {{l_0}\Delta T}}α=l0​ΔTΔl​

l1α1ΔT=l2α2ΔT{l_1}{\alpha _1}\Delta T = {l_2}{\alpha _2}\Delta Tl1​α1​ΔT=l2​α2​ΔT

l1α1=l2α2{l_1}{\alpha _1} = {l_2}{\alpha _2}l1​α1​=l2​α2​

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