Question

Two wires of equal lengths are mode of the same materil. Wire A has a diameter that is twice as that of wire B. If the identical weights are suspended from the ends of these wires, the increase in length is.

• A. Four times for wire A as for wire B.
• B. Twice for wire A as for wire B.
• C. Half for wire A as for wire B.
• D. One-fourth for wire A as for wire B.

Answer 1

The correct option is D One-fourth for wire A as for wire B.

$\Delta l=\frac{Fl}{AY}$
$\Rightarrow \Delta l\propto \frac{1}{r^2}$(F, l and Y are same)
$\frac{\Delta l_A}{\Delta l_B}={\left[\frac{r_B}{r_A}\right]}^2={\left[\frac{r_B}{2r_B}\right]}^2=\frac{1}{4}$
or $4\Delta l_A=\Delta l_B$