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Two wires are made of the same metal. The length of the first wire is half that of the second and its diameter is double that of the second wire. If equal loads are applied on both wires, find the ratio of increase in their lengths?
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Two wires are made of the same metal. The length of the first wire is ...

since two wires are identical therefore youngs modulus of both the wire is same.
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Two wires are made of the same metal. The length of the first wire is ...
Given information:

Two wires made of the same metal.
Length of the first wire is half that of the second wire.
Diameter of the first wire is double that of the second wire.
Equal loads are applied on both wires.

Understanding the problem:

We need to find the ratio of increase in the lengths of the two wires when equal loads are applied.

Solution:

Let's assume the length of the second wire as 'L' units. Therefore, the length of the first wire is 'L/2' units.

Calculating the increase in length:

We know that the increase in length of a wire is directly proportional to the load applied and inversely proportional to the cross-sectional area of the wire.

Since equal loads are applied on both wires, the increase in length of the first wire (ΔL1) is equal to the increase in length of the second wire (ΔL2).

Calculating the cross-sectional area:

The cross-sectional area of a wire is directly proportional to the square of its diameter.

Let's assume the diameter of the second wire is 'd' units. Therefore, the diameter of the first wire is '2d' units.

The cross-sectional area of the second wire (A2) is π(d/2)^2 = πd^2/4 square units.
The cross-sectional area of the first wire (A1) is π(2d/2)^2 = π(4d^2)/4 = πd^2 square units.

Calculating the ratio of increase in length:

Since the increase in length of the first wire (ΔL1) is equal to the increase in length of the second wire (ΔL2), we can write:
ΔL1/L1 = ΔL2/L2

Let's substitute the values:
ΔL1/(L/2) = ΔL2/L

Cross-multiplying the equation:
2ΔL1 = ΔL2

Therefore, the ratio of increase in their lengths is:
ΔL1 : ΔL2 = 1 : 2
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Two wires are made of the same metal. The length of the first wire is half that of the second and its diameter is double that of the second wire. If equal loads are applied on both wires, find the ratio of increase in their lengths?
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