Question

When a certain weight is suspended from a long uniform wire, its length increases by $1cm$. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, the increase in length will be

• A. $0.5cm$
• B. $2cm$
• C. $4cm$
• D. $8cm$

Answer 1

The correct option is C $4cm$

$Y=\frac{Fl}{a△l}$ or $△l\propto \frac{1}{a};△l\propto \frac{1}{D^2}$
$\frac{△l_2}{△l_1}=\frac{D_1^2}{D_2^2}=4$ or $△l_1=4△l_1=4cm$.