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Two wire are made of same material and have same volume However wire 1 has cross-sectional area A and wire 2 has cross-sectional area 3A. If length of wire 1 is increased by $\Delta x$ on applying force F, how much force is needed to stretch wire 2 by same amount

\[\begin {array} {1 1} (a)\;4\;F \\ (b)\;6\;F \\ (c)\;9\;F \\ (d)\;F \end {array}\]

1 Answer

Since the two wires have same volume.
Length of wire 1 $=l$
Length of wire 2 $=\large\frac{l}{3}$
Area of wire 1 $=A$
Area of wire 2 $=3A$
wire 1:
$Y=\large\frac{F/A}{\Delta x /l}$---------(1)
wire 2:
$Y=\large\frac{F'/A}{\Delta x /l/3}$-------------(2)
from (1) and (2)
$\large\frac{F}{A} \times \frac{l}{\Delta x}=\frac{F^1}{3A} \times \frac{l}{3 \Delta x}$
Hence c is the correct answer.


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