When a 125-kg piece of equipment is hung from a steel wire of diameter 6.00 mm, it stretches the wire by 4.00 mm. If instead the wire had a diameter of 3.00 mm, but all else were the same, by what distance would the same equipment stretch the wire?
A) 4.00 mm
B) 2.00 mm
C) 1.00 mm
D) 16.0 mm
E) 8.00 mm

Question

When a 125-kg piece of equipment is hung from a steel wire of diameter  6.00 mm, it stretches the wire by  4.00 mm. If instead the wire had a diameter of  3.00 mm, but all else were the same, by what distance would the same equipment stretch the wire?
A)  4.00 mm
B)  2.00 mm
C)  1.00 mm
D)  16.0 mm
E)  8.00 mm

Quizplus · Accepted Answer

The stretch in the wire due to the hanging equipment is inversely proportional to the cross-sectional area of the wire. When the diameter is halved (from 6.00 mm to 3.00 mm), the area (πr^2) is reduced by a factor of 4 (since area depends on the square of the radius, and halving the diameter halves the radius). Therefore, for a wire with one-fourth the cross-sectional area, the stretch would be four times as much, making the correct answer 4.00 mm * 4 = 16.0 mm.

When a 125-Kg Piece of Equipment Is Hung from a Steel