In an experiment to determine Young's Modulus for a wire, several loads are attached to the wire and the corresponding extension measured. The tensile stress in each case depends on the
A
load and the extension
B
load and the radius of the wire
C
radius of the wire and the extension
D
extension and the original length of the wire
Verified Correct Answer: B.
Physical Principles & Numerical Solution
In an experiment to determine Young's Modulus for a wire, the tensile stress depends on the following factors:
Tensile Stress = The tensile stress (\( \sigma \)) is defined as the force (load, \( F \)) applied per unit area (\( A \)):
\(\sigma = \frac{F}{A}\)
Cross-Sectional Area:
For a wire with a circular cross-section, the area (\( A \)) can be expressed in terms of the radius (\( r \)):
\(A = \pi r^2\)
Combining the Equations:
Therefore, the tensile stress can be rewritten as:
\(\sigma = \frac{F}{\pi r^2}\)
From this, we see that the tensile stress depends on both the load (\( F \)) and the radius (\( r \)) of the wire.
Thus, the correct answer is:
\(\text{B. Load and the radius of the wire}\)
Source: Myschool Past Questions Archive (Record #28053)