Select the correct answer.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

Nothing is changed but the length of the wire.

To determine the correct answer to this question, we need to understand the factor that influences the change in length of a steel wire under an applied load. The change in length of a wire can be calculated using Hooke's Law, which states that the change in length (ΔL) is directly proportional to the applied load (F) and the material property known as Young's modulus (E).

So, the equation for the change in length of a wire (ΔL) is given by:

ΔL = (F * L) / (A * E)

Where:
- ΔL is the change in length of the wire
- F is the applied load
- L is the original length of the wire
- A is the cross-sectional area of the wire
- E is the Young's modulus of the material

Now, let's examine each option provided:

A. A different material having a Young's modulus half that of steel:
If we use a different material with a Young's modulus half that of steel, the ΔL will not be halved. The change in length is directly proportional to the Young's modulus. Therefore, this option is not correct.

B. Half the cross-sectional area of the steel wire:
According to the equation, ΔL is inversely proportional to the cross-sectional area of the wire (A). If we halve the cross-sectional area of the steel wire, the change in length will be halved, keeping all other conditions constant. Therefore, this option is correct.

C. Half the length of steel wire:
If we halve the length of the steel wire, the change in length will also be halved. However, the question specifies that we need to keep all other conditions constant. So, changing the length is not a viable option in this context. Therefore, this option is not correct.

D. Half the radius of the steel wire:
The cross-sectional area (A) is directly related to the square of the radius (r) of the wire. If we halve the radius of the steel wire, the cross-sectional area will decrease by a factor of 4 (radius squared). Therefore, this option is not correct as it does not result in halving the change in length.

In conclusion, the correct answer is B. Halving the cross-sectional area of the steel wire while keeping all other conditions constant will halve the change in length of the wire under an applied load.