Two wires, P and Q, are made from the same metal and hang vertically from a steel girder.
Wire Q has half the length and twice the diameter of wire P.
Identical masses are attached to the bottom of each wire. Both wires obey Hooke’s law as they are stretched by the weight of the masses.
What is the ratio extension of wire Q / extension of wire P?
A 8 / 1
B 4 / 1
C 1 / 1
D 1 / 2
ANSWER: A
The Physics Behind
- One version of Hooke's Law is given by the following equation
Y = stress / strain
where Y is constant called Young modulus,
stress = force F / area A, and strain = extension x / original length L
- Substituting all the other equation to Hooke's Law equation,
Y = FL/Ax
x = FL/AY
- Assume that x is the extension of wire Q. For the extension X of wire P which has half L and 2D,
X = F(0.5)L/4AY
[where F and Y are same in both wires]
X = 8 FL/AY
X = 8x
- Therefore, the ratio being asked is
8x/x
[or option A]
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