Question

Two wires of lengths $l$ and $2l,$ radii $r$ and $2r$ respectively having same Youngs modulus are hung with a weight $mg$. Net elongation is

• A. $\frac{3mgl}{-\pi r^{2}Y}$
• B. $\frac{2mgl}{3\pi r^{2}Y-}$
• C. $\frac{3mgl}{-2\pi x^{2}Y}$
• D. $\frac{3mgl}{-4\pi r^{2}Y-}$

Answer 1

Answer: (C)

Youngs modulus, $Y=\frac{mgl}{a_1{l}_1}$
$\therefore l_1=\frac{mgl}{Y\pi r^2}$ ... (i)
and $Y=\frac{mg(2l)}{a_2{l}_2}=\frac{mg(2l)}{\pi (2r{)}^2{l}_2}$
or $l_2=\frac{mgl}{2Y\pi r^2}$ ... (ii)
From Eqs. (i) and (ii), we have
$\therefore l_1+l_2=\frac{mgl}{Y\pi r^2}+\frac{mgl}{2Y\pi r^2}=\frac{3}{2}\frac{mgl}{Y\pi r^2}$