The change in length of a steel wire under an applied load can be halved by keeping all other conditions constant but using:

A. a different material having a Young's modulus half that of steel
B half the cross sectional area of the steel wire
C half the length of steel wire
D half the radius of the steel wire

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A Piece of material 15 cm long by 2.5 cm square is in compression under a load 100 KN. If the modulus of elasticity of the material s 105 GPa and Poisson’s ratio is 0.25, find the alteration in length if all lateral strain is prevented by the application of uniform lateral external pressure of suitable intensity.

To find the option that will result in a halving of the change in length of the steel wire under an applied load, we need to consider Hooke's Law.

Hooke's Law states that the change in length of a material is directly proportional to the applied force and inversely proportional to the material's Young's modulus and cross-sectional area.

Let's evaluate each option:

A. A different material having a Young's modulus half that of steel:
If we use a material with a Young's modulus half that of steel, the change in length will be halved. This is because the Young's modulus is in the denominator in the equation for the change in length. Therefore, option A is a valid choice.

B. Half the cross-sectional area of the steel wire:
If we decrease the cross-sectional area, the change in length will actually double. According to Hooke's Law, the change in length is inversely proportional to the cross-sectional area. So, option B is not correct.

C. Half the length of the steel wire:
Changing the length of the wire will not affect the change in length as per Hooke's Law. Therefore, option C is not correct.

D. Half the radius of the steel wire:
If we halve the radius of the wire, the cross-sectional area will be reduced to a quarter of its original value. According to Hooke's Law, the change in length is inversely proportional to the cross-sectional area. So, by halving the radius, the change in length will be doubled. Therefore, option D is not correct.

In conclusion, the correct answer is:

A. A different material having a Young's modulus half that of steel.

To determine the correct option to halve the change in length of a steel wire under an applied load while keeping all other conditions constant, we need to understand the relationship between the change in length and the variables involved.

The change in length of a wire under an applied load is given by the equation:

ΔL = (F * L) / (A * E),

where ΔL is the change in length, F is the applied force, L is the original length of the wire, A is the cross-sectional area of the wire, and E is the Young's modulus of the material.

Let's evaluate each option to see how it affects the change in length:

A. Using a different material having a Young's modulus half that of steel.
If we use a material with a Young's modulus half that of steel, the change in length equation becomes:

ΔL = (F * L) / (A * (E/2)) = 2 * (F * L) / (A * E)

Therefore, using a different material does not halve the change in length. This option is incorrect.

B. Using half the cross-sectional area of the steel wire.
If we half the cross-sectional area of the steel wire, the change in length equation becomes:

ΔL = (F * L) / ((A/2) * E) = 2 * (F * L) / (A * E)

Again, this option does not halve the change in length. This option is incorrect as well.

C. Using half the length of the steel wire.
If we halve the length of the steel wire, the change in length equation becomes:

ΔL = (F * (L/2)) / (A * E) = (F * L) / (2 * A * E)

This option does halve the change in length. We have found the correct option.

D. Using half the radius of the steel wire.
If we halve the radius of the steel wire, the change in length equation becomes:

ΔL = (F * L) / (((π * (r/2)^2)) * E) = (F * L) / ((π * r^2 * E)/4) = 4 * (F * L) / (π * r^2 * E)

Halving the radius does not halve the change in length. This option is incorrect.

Therefore, the correct option to halve the change in length of a steel wire under an applied load while keeping all other conditions constant is option C: half the length of steel wire.