A wire of circular cross section of diameter d and length L is stretched an amount $\Delta$L by a steady force F.An equal force would produce how much stretch in a similar wire of diameter 2d and length 2L?
A)$\Delta$L/8
B)$\Delta$L/4
C)$\Delta$L/2
D)2$\Delta$L
E)4$\Delta$L

Question

Quizplus · Accepted Answer

The stretch of a wire is directly proportional to the force applied and inversely proportional to its length and directly proportional to its cross-sectional area. So, if the diameter of the wire is doubled (i.e. its cross-sectional area is quadrupled) and the length is also doubled, then the new wire will have 8 times the cross-sectional area of the original wire. Therefore, the force required to produce the same stretch will be 8 times less. Thus, the stretch produced by the same force applied to the new wire will be 1/8th of the stretch produced in the original wire. So, the answer is F1F1F1S1F1F1F10L/2.

A Wire of Circular Cross Section of Diameter D and Length