A string $A$ of length $0.314$ m and Young's modulus $2 \times 10^{10}\ \text{N/m}^2$ is connected to another string $B$ of length and Young's modulus both twice of those of $A$. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass $0.8$ kg. The net change in length of the combination is ______ mm.
(radius of both the strings is $0.2$ mm and acceleration due to gravity $= 10\ \text{m/s}^2$) (Mass of both strings is to be neglected as compared to the mass of load)
Answer: (B) $2$
Concept. In series both strings carry the full load; add the two extensions $\dfrac{FL}{AY}$.
Step 1. Area and load. $A=\pi(2\times10^{-4})^2=1.257\times10^{-7}$ m$^2$; $F=8$ N.
Step 2. String A. $\dfrac{8\times0.314}{1.257\times10^{-7}\times2\times10^{10}}=1.0\times10^{-3}$ m.
Step 3. String B. Length and $Y$ both doubled: the same $1.0$ mm.
Step 4. Total. $2$ mm.
Answer. Option B.
Solution by Sreeraj P, M.Sc Physics
