Question

A steel wire of diameter $0.5mm$ and Young’s modulus $2\times 10^{11}N{m}^{-2}$ carries a load of mass $M$. The length of the wire with the load is $1.0m$. A vernier scale with $10$ divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count $1.0mm$, is attached. The $10$ divisions of the vernier scale correspond to $9$ divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by $1.2kg$, the vernier scale division which coincides with a main scale division is __________. Take $g=10m{s}^{-2}$ and $\pi$ =

Answer 1

Answer: 3

$d=0.5mm$
$Y=2\times 10^{11}l=1m$
$\Delta l=\frac{Fl}{Ay}=\frac{\frac{mgl}{\pi d^2}}{4}y$
$=\frac{1.2\times 10\times 1}{\frac{\pi }{4}\times {\left(5\times 10^{-4}\right)}^2\times 2\times 10^{11}}$
$\Delta l=\frac{1.2\times 10}{\frac{3.2}{4}\times 25\times 10^{-8}\times 2\times 10^{11}}$
$=\frac{12}{0.8\times 25\times 2\times 10^3}=\frac{12}{40\times 10^3}=0.3mm$
So $3^{rd}$ division of a vernier scale will coincide with main scale.