A thick brass wire of length ' $\mathrm{L}$ ' and density ' $\rho$ ' is suspended from rigid support. Due to…
A thick brass wire of length ' $\mathrm{L}$ ' and density ' $\rho$ ' is suspended from rigid support.
Due to its own weight, $' \ell^{\prime}$ is the increase in length. Young's modulus ' $\mathrm{Y}^{\prime}$ of brass wire in terms of density is
$(\mathrm{g}=$ acceleration due to gravity)
$\mathrm{Y}=\frac{\rho \mathrm{gL}}{4 \ell}$
$\mathrm{Y}=\frac{\rho \mathrm{gL}^{2}}{4 \ell}$
$\mathrm{Y}=\frac{\rho \mathrm{gL}}{3 \ell}$
$\mathrm{Y}=\frac{\rho \mathrm{gL}^{2}}{\ell}$
Solution
$Y=(F / A) \cdot(L / \Delta L) \quad(\because \Delta L=l)$
$=\frac{M g L}{A \Delta L}$
$=\frac{\rho g L^{2}}{l} (\because M=\rho A l)$
$\because$ (option 4 is correct)