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The ratio of the coefficient of linear expansion of two meta...

The ratio of the coefficient of linear expansion of two metals 1/2 is 3:4. If, when heated through the same temperature change, the ratio of the increase in length of the two metals, e1/e2 is 1:2, the ratio of the original lengths l1/l2 is

A.

8/3

B.

3/2

C.

2/3

D.

3/8

Correct answer is C

Ratio of their linear expansion = 1/2= 3:4.
When heated to the same temperature range, the ratio of their increase in length e1/e2 = 1:2
But the increase in length of
1 = e1 = ∝1l1Δθ and increase i length of
2 = e2 = ∝2l2Δθ

=> e1 = 1l1Δθ = 1l1 = 1
e22l2Δθ2l22

But 1 = 3, ∴3xl1=1
244l22

=> 6l1 = 4l2
l1=4=2OR 2 : 3
l263