Elasticity

For a wire under tension, the elongation is given by: where: is the force, is the length of the wire, is the cross-sectional area, and is the Young's modulus. Since the elongation is the same for both wires, we can equate the elongations: The cross-sectional area , so: Thus, we find:

The tension in a soap film can be calculated using the following formula: where is the weight supported by the film and is the length of the slider. Substituting the values:
Thus, the correct answer is (d).

The work done in stretching a wire is given by:

where is the work, is the force, is the Young's modulus, and is the cross-sectional area of the wire. The force required to stretch the wire is related to the cross-sectional area and the material's Young's modulus. Since the radius of the wire is doubled and the length is halved, the cross-sectional area is quadrupled (since , and the radius is doubled). The work done is proportional to both the cross-sectional area and the square of the length. Hence, changing the dimensions of the wire affects the work required to stretch it.

Using these relationships and applying them to the second wire, we find that the work required is 8 J.

Hence, the correct answer is (b).