Q 11-08-005NEETJEE MainMedium
Two wires P and Q are made of the same material. The length of Q is twice that of P, and the diameter of P is twice that of Q. The same load is hung from each. The ratio of the extension of P to that of Q is
Answer: (B) $1 : 8$
Concept. $\Delta L = \dfrac{FL}{AY}$ with $A = \dfrac{\pi d^2}{4}$. Same material and load, so $\Delta L \propto \dfrac{L}{d^2}$.
Step 1. Set up. P: length $L$, diameter $2d$. Q: length $2L$, diameter $d$.
Step 2. Ratio.
$$\frac{\Delta L_P}{\Delta L_Q} = \frac{L/(2d)^2}{2L/d^2} = \frac{1/4}{2} = \frac18$$
Answer. $1 : 8$ (Option B).
Solution by Sreeraj P, M.Sc Physics