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. What is the mass of the load that can be supported by the thicker cable if it stretches by an amount d?
A)M/4
B)M/2
C)M
D)2M
E)4M

Question

Quizplus · Accepted Answer

The stretching of the cable is related to its cross-sectional area. Since the diameter is doubled, the area increases by a factor of four (since area is proportional to the square of the diameter). Therefore, the thicker cable can support four times the mass while stretching by the same amount.

A Cable Stretches by an Amount D When It Supports