two wires A and B have Youngsmodlii in the ratio of length's is 1:2 and ratio of length's is 1:1 .Under the application of same stress the rato of elongations is ----

ans
1.)2:1

To solve this problem, we need to use the concept of Young's modulus and the relationship between stress, strain, and length.

1. Young's modulus (Y) is a measure of the stiffness or elasticity of a material. It is given by the formula: Y = stress/strain.

2. Stress (σ) is the force applied to a material divided by its cross-sectional area. Mathematically, stress = force/area.

3. Strain (ε) is the ratio of the change in length to the original length of a material. It can be expressed as: strain = ΔL/L, where ΔL is the change in length and L is the original length.

4. Based on the given information, let's assume that the stress applied to both wires (A and B) is the same.

Now, let's calculate the ratio of elongations for wires A and B:

For wire A:
Let the original length be L1.
Stress on wire A = stress on wire B

According to Young's modulus formula: Y1 = stress/strain A = stress/((ΔL1/L1)A)
Similarly, for wire B: Y2 = stress/((ΔL2/L2)B)

Given that Y1/Y2 = 1/2 (ratio of Young's moduli)
=> Y1/Y2 = (stress/((ΔL1/L1)A))/(stress/((ΔL2/L2)B))
=> Y1/Y2 = ((ΔL2/L2)B)/((ΔL1/L1)A)

Also given that L1: L2 = 1:1 (ratio of lengths) for wire A and wire B.

Let's substitute L1 = L2 = L into the equation:
=> Y1/Y2 = ((ΔL2/L)/(ΔL1/L))
=> Y1/Y2 = (ΔL2/ΔL1)
=> ΔL2/ΔL1 = Y1/Y2 = 1/2

Therefore, the ratio of elongations for wire A and wire B is 2:1.

So, the answer is 2:1.