Mechanical Properties Of Solids Question 5
Question 5 - 2024 (29 Jan Shift 2)
A wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$, its length increases by $l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become.
(1) 3 times
(2) $3 / 2$ times
(3) 4 times
(4) 2 times
Show Answer
Answer: (4)
Solution:
$Y=\frac{\text { stress }}{\text { strain }}$
$Y=\frac{\frac{F}{\frac{\ell}{2}}}{\frac{\ell}{L}}$
$F=Y \pi r^{2} \times \frac{\ell}{L}$.
$Y=\frac{\frac{Fr / 2}{\frac{\Delta \ell}{2}}}{L}$
$F=Y \frac{\Delta \ell}{L} \times 2 \times \frac{\pi r^{2}}{4}$
From (i)
$Y \pi r^{2} \frac{\ell}{L}=Y \frac{\Delta \ell}{L} \frac{\pi r^{2}}{2}$
$\Delta \ell=2 \ell$
