Q. Two wires of equal lengths are made of the same material. Wire $A$ has a diameter that is twice as that of wire $B$. If 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 $B$
Explanation
(d) $l = \frac{FL}{AY} \Rightarrow l \propto \frac{1}{r^{2}}\lbrack F,L\ and\ Y\ are\ same\rbrack$
$\frac{l_{A}}{l_{B}} = \left( \frac{r_{B}}{r_{A}} \right)^{2} = \left( \frac{r_{B}}{2r_{B}} \right)^{2} = \frac{1}{4} \Rightarrow l_{A} = 4l_{B}\ or\ l_{B} = \frac{l_{A}}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.