Question

A wire of cross-sectional area $A$ breaks due to its own weight when length of a wire is $l$. If area of cross-section of the wire is made $3A$ then maximum length of the wire can be hung without breaking is

• A. $3l$
• B. $2l$
• C. $1.5l$
• D. $l$

Answer 1

The correct option is D $l$

$\begin{array}{c}\text{Given,}\\ \text{wire breaks due to own weight}\\ \text{cross sectional}\text{Area}=A\\ \text{length of wire}=\ell \end{array}$

$\text{So, Breaking strength of wire}=\frac{\text{weight}}{A}$

$\begin{array}{c}\text{Let}\rho \text{(density) of wire}\\ \text{then}\mathrm{mass}=\rho \text{.volume}\end{array}$

$m=\rho \cdot A\cdot l$

$\therefore \text{weight}=mg=\rho Alg$

$\text{So, Braking Strength of wire}=\frac{\rho Alg}{A}$

$=\rho lg-\left(i\right)$

$\begin{array}{c}\text{Now, when}A\text{become}34\text{but braking}\\ \text{strength remain same then}\end{array}$

$\begin{array}{c}\text{B.S.}=\frac{3\rho A{L}^{{}^{\prime }}g}{3A}\\ \text{B.S}=\rho g{L}^{{}^{\prime }}--\text{(ii)}\end{array}$

$\begin{array}{c}\text{equation}\left(i\right)=\left(ii\right)\\ L=l\end{array}$