Q. A wire of length $L$ suspended vertically from a rigid support is made to suffer extension $l$ in its length by applying a force $F$. The work is
A) $\frac{Fl}{2}$
B) $Fl$
C) $2Fl$
D) $Fl$
Explanation
(a) $dW = Fdl$
$W = \int_{0}^{l}{F\ dl}\ \ \ Y = \frac{FL}{dl}$
or $W = \int_{0}^{l}{\frac{Y\ al}{L}dl}\ \ or\ \ F = \frac{Y\ al}{L}$
or $W = \frac{Ya}{L}\int_{0}^{l}{dl}\ \ or\ \ \ W = \frac{Ya}{L}\left( \frac{l^{2}}{2} \right)$
or $W = \frac{1}{2}\frac{Y\ al}{L}l = \frac{1}{2}Fl$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.