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