Question

When a certain weight is suspended from a long uniform wire, its length increases by $1\text{cm}$. 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 in cm will be

Answer 1

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