A cable stretches by an amount d when it supports a crate of mass M. The cable is replaced by another cable of the same material having the same length and twice the diameter. If the same crate is supported by the thicker cable, by how much will the cable stretch?
A)d/4
B)d/2
C)d
D)2d
E)4d

Question

Quizplus · Accepted Answer

The stretch of a cable is inversely proportional to its cross-sectional area. Doubling the diameter increases the area by a factor of four (since area is proportional to the square of the diameter), so the stretch is reduced by a factor of four. Thus, the new stretch is d/4.

A Cable Stretches by an Amount D When It Supports