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Q.

Two bars A and B of circular cross section, same volume and made of the same material, are subjected to tension. If the diameter of A is half that of B and if the force applied to both the rod is the same and it is in the elastic limit, the ratio of extension of A to that of B will be

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a

16

b

8

c

4

d

2

answer is A.

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Detailed Solution

We have, Y=FlaΔl⇒ Y=Fa×lΔl Now, V=al  or  l=Va ∴Y=FVa2Δl         Δl∝1a2 or Δl∝1D4ΔlAΔlB=DB4DA4=14124=16
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Two bars A and B of circular cross section, same volume and made of the same material, are subjected to tension. If the diameter of A is half that of B and if the force applied to both the rod is the same and it is in the elastic limit, the ratio of extension of A to that of B will be