Question

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

Answer 1

Two bars A and B are of same material. So Modulus of elasticity is same for both. That is 'Y' is same.

Initially both bars are of same volume. That is length and cross section area are same.

Thus, r₁=r₂ initially.

[r₁= Radius of bar A and r₂= radius of bar B]

When r₁ is made half of r₂, keeping the force applied on the both bar same,  r₁= r₂/2

Let L= initial length of the both bar

For bar A, Y= {F/π(r₂/2)²}/{Δl₁/L}

                  Δl₁=(4F.L)/{Yπ(r₂)²}----- (1)

For bar B, Y= (F.L)/Δl₂π(r₂)²

                Δl₂= (F.L)/{Yπ(r₂)²}----- (2)

Now (1)÷ (2)=> Δl₁/Δl₂= 4/1

Δl₁=4Δl₂

Answer 2

Explanation:

1/4*1/4=1/16

xa/xb=16