Question

Spring constant of a spring varries as: [where Young's Modulus, $l=1$ length, $d=$ diameter of spring wire]

• A. $\propto \frac{1}{\gamma }$
• B. $\propto d^2$
• C. $\propto l$
• D. $\propto {\gamma }^2$

Answer 1

Answer: (B)

$F=-K\Delta \ell$ and $\gamma =\frac{F}{A}/\frac{\Delta \ell }{\ell }=F=\gamma A\times \frac{\Delta \ell }{\ell }$
$=\left(\frac{\gamma \pi d^2}{4\ell }\right)\Delta \ell \Rightarrow k\propto \gamma d^2/\ell$