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. $\frac{3 m g l}{-\pi r^{2} Y}$
• B. $\frac{2 m g l}{3 \pi r^{2} Y-}$
• C. $\frac{3 m g l}{-2 \pi x^{2} Y}$
• D. $\frac{3 m g l}{-4 \pi r^{2} Y-}$

Answer 1

Answer: (C)

Youngs modulus, $Y=\frac{m g l}{a_{1} l_{1}}$
$\therefore l_{1}=\frac{m g l}{Y \pi r^{2}}$ ... (i)
and $Y=\frac{m g(2 l)}{a_{2} l_{2}}=\frac{m g(2 l)}{\pi(2 r)^{2} l_{2}}$
or $l_{2}=\frac{m g l}{2 Y \pi r^{2}}$ ... (ii)
From Eqs. (i) and (ii), we have
$\therefore l_{1}+l_{2}= \frac{m g l}{Y \pi r^{2}}+\frac{m g l}{2 Y \pi r^{2}}=\frac{3}{2} \frac{m g l}{Y \pi r^{2}}$