If the work done in stretching a wire by 1 mm is 2 J, the work necessary for stretching another wire of same material but with double radius of cross-section and half the length by 1 mm is

Question

Dr. Abubacker · Accepted Answer

(d) $W = \frac{1}{2}\ F\mathrm{\Delta}l$
$\binom{W = \frac{1}{2} 	imes \ \frac{Y\pi r^{2}\mathrm{\Delta}l}{l}\ \mathrm{\Delta}l}{or\ W = \ \frac{Y\pi r^{2}\mathrm{\Delta}l}{2l}}\left| \begin{array}{r}
Y = \frac{Fl}{\pi r^{2}\mathrm{\Delta}l} \
F = \frac{Y\pi r^{2}\mathrm{\Delta}l}{l}\ 
\end{array} ight.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ $ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ $
Or $W\  \propto \frac{r^{2}}{l},\ W\  \propto \frac{\left( 2r^{2} ight)^{2}2}{l}$
$\frac{W^{'}}{W} = 8\ \ \ or\ W^{'} = 8 	imes 2\ J = 16\ J$

Q. If the work done in stretching a wire by 1 mm is 2 J, the work necessary for stretching another wire of same material but with double radius of cross-section and half the length by 1 mm is

Explanation

Reviewed by Dr. Abubacker

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